The 22-year-old ended the 2021-22 season with 34 goals in all competitions and is allegedly set to command a mammoth €100m (£85.4m) to leave Portugal this summer.
Such a transfer would smash the Liverpool transfer record previously set by Virgil van Dijk, but where would Nunez's nine-figure arrival rank among his compatriots?
Using data from Transfermarkt, Sports Mole counts down the 10 most expensive Uruguayan players of all time.
10. Nahitan Nandez - £14.6m
Following breakthroughs in his native South America with Penarol - Nunez's former team in his homeland - and Boca Juniors, Nahitan Nandez earned himself a £14.6m transfer to Serie A regulars Cagliari in the summer of 2019.
Immediately cementing himself as a starter, the versatile 26-year-old - who can feature on the right, left or centre of the midfield if called upon to do so - has already racked up four goals and nine assists in 94 appearances for Cagliari over the past three years.
Nandez's strong numbers for the Italian side led to brief links with Tottenham Hotspur some months ago, and he will likely be a man in demand this summer following Cagliari's relegation to the second tier.
9. Martin Caceres - £14.9m
Veteran defender Martin Caceres is the true definition of a well-travelled player, and it is often easy to forget that the 35-year-old was once on the books at Barcelona, who forked out £14.9m to sign him from Villarreal in 2008.
However, Caceres's switch to Catalonia did not work out as intended - he only made 23 appearances for the club in all competitions and was loaned out to Juventus and Sevilla, eventually joining the latter for just £2.7m three years later.
The 113-cap Uruguay international still collected a Champions League winners' medal in 2009 and would enjoy a trophy-laden spell with Juventus between 2012 and 2016, and he can now be found plying his trade in La Liga with Levante, but his contract is up in a couple of weeks' time.
8. Diego Laxalt - £17.1m
Something of a forgotten name nowadays, Diego Laxalt had no qualms about signing for AC Milan despite his previous stint with city rivals Inter Milan, and the Rossoneri coughed up £17.1m to sign him from Genoa in 2018.
Laxalt would only feature for Milan 35 times in three seasons, providing one assist and being shipped out on loan to Torino and Celtic in that time before the Serie A champions cut their losses last summer.
The 29-year-old left-back joined Dynamo Moscow for a measly £3.2m in 2021, and he has not earned a call-up to the national team since before COVID-19 times in 2019.
7. Diego Forlan - £18.9m
The less said about Diego Forlan's Manchester United spell the better, but Spain is where the legendary striker thrived, and Atletico Madrid took their chances on him in 2007 - paying Villarreal £18.9m in the process.
Forlan's stint in the capital was a wholly successful one - the Uruguayan took the Pichichi Trophy with 32 goals in 2008-09, scored both goals in Atletico's 2010 Europa League final win over Fulham and won the Golden Ball at the 2010 World Cup.
Forlan ended his Atletico spell in 2011 to sign for Inter Milan, and the forward would proceed to test himself in Brazil, India, Japan and Hong Kong before hanging up his boots in 2019.
6. Rodrigo Bentancur - £19.5m
The first of two players who technically features twice on this list, Rodrigo Bentancur's £17.1m Juventus arrival as a fresh-faced 20-year-old in the summer of 2017 would already earn him a place in the top 10.
While he would feature regularly for the Old Lady and add three Serie A titles to his CV, Bentancur would fail to nail down a regular starting spot in late 2021, and the pull of Antonio Conte and Tottenham was too strong to ignore.
Tottenham paid £19.5m to prise Bentancur away from Turin, and to say the move has worked out well would be an understatement, with the 24-year-old playing an integral role in his side's successful push for a Champions League berth.
5. Matias Vecino - £21.6m
Matias Vecino's time at Inter Milan is coming to an end, but the lynchpin has been a faithful servant to the Nerazzurri during his five years at the club, with Fiorentina receiving £21.6m for his services in 2017.
Vecino has amassed 13 goals and seven assists in 127 games from the middle of the park for Inter, although he only made two Serie A starts last term as Marcelo Brozovic, Nicolo Barella and Hakan Calhanoglu held the fort.
The 30-year-old's contract with Inter expires at the end of the month, and Lazio are seemingly in pole position to snap up the experienced South American on a free transfer this summer.
4. Darwin Nunez - £21.6m
He may be about to become one of the most expensive players of all time, but Darwin Nunez is already high up on Uruguay's list after also commanding a £21.6m fee to leave Almeria in 2020.
Interest in Nunez's services was rife before he settled on Benfica, during which time he has scooped the Primeira Liga Golden Boot and reached the Champions League quarter-finals - netting twice against Liverpool in the process.
The 6ft 1in striker is apparently set to snub interest from Manchester United to link up with Jurgen Klopp's side, assuming that the Reds will bow to Benfica's demands, but their most recent signing from Portugal - Luis Diaz - has worked out pretty well.
3. Lucas Torreira - £25.8m
While he was not exactly the same build as Patrick Vieira, Lucas Torreira - all 5ft 4in of him - made such a bright start to his Arsenal career, and his market value would seemingly only increase after his £25.8m departure from Sampdoria.
Scoring his first goal for the club against Tottenham Hotspur only increased his standing with the Emirates crowd, but Mikel Arteta ultimately preferred other options in the middle of the park, and Torreira was also struck with personal tragedy last year following the death of his mother.
However, Torreira has reignited his career on loan at Fiorentina, who have been expected to fork out around £12.5m to sign him permanently, but the 26-year-old's agents may have to start putting the feelers out after such a switch reportedly fell through.
2. Edinson Cavani - £58.1m
Sometimes, you get what you pay for in football.
After three goal-laden years at Napoli, Edinson Cavani was the subject of a £58.1m bid from Paris Saint-Germain in the summer of 2013. Napoli took the cash and ran, while PSG found their new history-maker.
Cavani's move to Paris signalled a new French football record for a transfer at the time, and the Uruguayan would play his part in six Ligue 1 title wins while racking up a club record 200 goals for the perennial champions.
Kylian Mbappe is expected to surpass that record quickly enough, and Cavani is now a free man after his mixed period at Manchester United drew to a close, but his advancing years and spate of injuries could hinder his chances of one final top-level move.
1. Luis Suarez - £73.6m
Still listed in the top 20 of the most expensive transfers of all time, Luis Suarez's £73.6m switch to Barcelona came after a simply phenomenal Liverpool spell that will perhaps be best remembered by rival fans for his tears at Selhurst Park.
Nevertheless, breaking the record for goals in a 38-game Premier League season with 31 strikes helped Suarez secure his dream switch to Barcelona, and he would ultimately register 194 goals for the Catalans while scoring at least 15 times in each La Liga season at Camp Nou.
Winning the Champions League and four La Liga titles did not prevent Suarez from departing in acrimonious circumstances for Atletico, but his powers had not faded, with 21 La Liga goals helping Los Rojiblancos finish at the top of the pile again.
A new chapter in Suarez's career will begin this summer, and a shock move to Aston Villa has been mooted, with fellow ex-Red Steven Gerrard jumping at the chance to reunite with the 35-year-old for one last swansong.
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