The Reds would need a favour from Steven Gerrard's Aston Villa at the Etihad in order for that to become a possibility, while they would also need to hold up their end of the bargain by ending an unforgettable domestic campaign on a high.
Regardless of what happens on Sunday - or indeed next Saturday when they face Real Madrid in the Champions League final - the 2021-22 season will live long in the memory of Liverpool fans.
Jurgen Klopp's men have taken their quadruple hunt as far as it is possible to go and, while they still may 'only' end up with the EFL Cup and FA Cup in their cabinet, they have at least made a clean sweep of trophies look more possible than any English club has ever done.
Of course, that dream is still alive courtesy of a come-from-behind 2-1 win at Southampton on Tuesday night, with Liverpool showcasing their strength in depth by making nine changes and still coming out on top only three days after a gruelling 120 minutes and penalty shootout against Chelsea in the FA Cup final.
The expectancy for Liverpool on Sunday will be one of disappointment, with the title very much in Man City's hands; victory for Pep Guardiola's men against Aston Villa will clinch them their fourth Premier League crown in five years, regardless of what Liverpool do.
Strange things can happen on the final day, though, and there is a certain degree of fatefulness about the prospect of Gerrard - arguably Liverpool's greatest ever player and certainly the best to have never won the title - finally securing the trophy for his boyhood club by providing some final-day drama to rival 1989 and 2012.
Incidentally, that 1989 campaign - when Arsenal pinched the title off Liverpool with victory at Anfield on the final day - was the last time that Liverpool lost their last game of the season when playing it at home, winning 13 and drawing two of the 15 such instances since.
Home or away, Liverpool have won five and drawn one of their final-day games under Klopp, and in the buildup to this one the German has stressed the importance of focusing solely on Wolves, rather than letting their minds drift to events at the Etihad.
Should they hold up their end of the bargain and pick up win number 28 of the season then they will finish the campaign on 92 points - their third-highest ever tally and one which would have been enough to win the title in 24 of the previous 29 Premier League seasons.
The formbook suggests that will be the case; Liverpool have won 15 of their last 17 Premier League games and are still unbeaten this calendar year, while they are on the verge of an unbeaten Premier League season at Anfield for a record-equalling fifth time.
Given their situation in the league, and the need for Man City to drop unlikely points, Liverpool could be forgiven for prioritising next Saturday's Champions League final in Paris - game number 63 of a relentless and exhausting season.
The failure to capitalise on any Man City slip-up is a galling prospect for them, though, and even if they do have one eye on Paris, they will be favourites to come out on top this weekend.
Liverpool have conceded just two league goals at Anfield since the turn of the year and have taken 37 points from the last 39 on offer in front of their own fans.
The 19-time champions of England also have a formidable record in this fixture, winning each of their last 10 Premier League meetings with Wolves and keeping eight clean sheets in that time.
By contrast, Wolves have lost 17 of their last 19 league games at Anfield, and their only two wins in that timeframe were separated by 26 years - it has been 12 years since their last.
Bruno Lage's side arrive at Anfield this time on their worst run of form this season, failing to win any of their last six games and picking up just two points from a possible 18 in that time.
That includes a 5-1 home defeat to Man City earlier this month, although they remain eighth in the table and are guaranteed another top-half finish - their third in the four seasons since being promoted.
Any improvement next season will likely depend on bringing more goals into the team - Wolves' tally of 37 goals scored is the fourth-lowest in the league, and Burnley in 2017-18 are the only team in Premier League history to have finished in the top eight having netted fewer.
There is little wrong at the other end, with only the top three conceding fewer, and it is that sturdy rearguard which is likely to be Liverpool's biggest hurdle in their attempts to come away with another three points.
However, Wolves have the joint-lowest win rate on the final day of the season of any current Premier League club, losing six and winning just one of their seven previous season-enders.
Another defeat on Sunday would keep Liverpool's unlikely title hopes alive, at which point Klopp will finally be able to turn his attention towards the Etihad and then Paris.
Liverpool's injury concerns had been beginning to mount as the games piled up at the end of the season, but Klopp has suggested that his squad should be in good shape for this match.
That issue has proven to be less serious than first feared, though, and Gomez will undergo tests in the next couple of days along with the others.
Klopp admitted that he would like all of the players to play in this game "for rhythm reasons" ahead of the Champions League final, but he is also unlikely to take any risks, particularly over key trio Salah, Van Dijk and Fabinho.
All three could feature from the bench at best, then, with Salah seemingly the most likely to be left out completely despite now only being one goal ahead of Son Heung-min in the Golden Boot standings.
Salah has made no secret of his desire for revenge against Real Madrid in the Champions League final and is unwilling to take any risks which could see him miss the huge showdown in Paris next week.
Mane is something of a final-day specialist too, having scored six goals in season-closing games before - only Harry Kane has more among currently active Premier League players.
Klopp may also give Divock Origi a fitting Anfield farewell at some stage of the match, having confirmed in his press conference that the club "legend" will leave when his contract expires this summer.
Wolves will still be without Max Kilman (ankle), Nelson Semedo (hamstring) and Romain Saiss (knee) for this final game of the season, but all three should be ready in time for the start of next season - should Saiss remain beyond the end of his current deal.
There has been growing speculation over the future of Ruben Neves, for whom Sunday's game could be a final Wolves outing, while his midfield partner Joao Moutinho could also be on his way out, with his contract expiring this summer.
Liverpool possible starting lineup:
Alisson; Alexander-Arnold, Matip, Konate, Robertson; Keita, Henderson, Thiago; Mane, Jota, Diaz
Wolverhampton Wanderers possible starting lineup:
Sa; Boly, Coady, Toti; Jonny, Neves, Moutinho, Dendoncker, Ait-Nouri; Jimenez, Neto
We say: Liverpool 2-0 Wolverhampton Wanderers
In many ways, Liverpool go into this match with nothing to lose, the expectancy being that Man City will win and anything else being a very welcome bonus.
Even so, they cannot afford to let their minds drift to the Champions League final just yet, and while he will not take any risks with his team selection, Klopp will nonetheless put out a team that he feels will win against Wolves.
Complacency very rarely creeps into Klopp's Liverpool, and with a host of first-teamers to return - and the fact that the result could mean a lot more to Liverpool than it does to Wolves - we are backing the Merseysiders to come away with the three points.
For additional data used by our team to analyse our suggested result please click here.
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