After enjoying a spectacular campaign with Domenico Tedesco's side in 2021-22, banking 35 goals and 20 assists in 52 games in all competitions, interest in Nkunku was rife.
Man United were heavily linked with a move for the 24-year-old during Ralf Rangnick's tenure, while Chelsea and Arsenal were also credited with an interest.
The Premier League trio were supposedly told to stump up offers of at least £100m for Nkunku, who has now signed a new deal with the Bundesliga side until 2026.
The France international agreed to the fresh terms last month, and the deal is also understood to include a release clause of €60m (£51.3m), which can be activated in 12 months' time.
As a result, the Manchester Evening News speculates that Man United could be among the clubs ready to trigger Nkunku's release clause at the end of next season.
Nkunku affirmed that his "story" at RB Leipzig was not finished after signing his new deal last month, telling the club website: "I'm pleased to continue wearing the RB Leipzig shirt.
"After our great achievement in winning the DFB-Pokal, it remained clear that my story here isn't over yet – we want more! I was really impressed with the club's efforts to keep me, so a big thanks goes to those responsible for the trust in me and especially to Oliver Mintzlaff, with whom I was always in close contact.
"RB Leipzig have made a name for themselves on the international stage in recent years and have shown time and again that we can compete for titles. We want to build on that going forward and go one step further."
The attacker has spent the last three years at the Red Bull Arena since leaving Paris Saint-Germain for a fee of £11.7m in 2019, and he has amassed 44 goals and 47 assists in 134 games for the club since.
Nkunku has also earned six caps for the France national team under Didier Deschamps, providing two assists, and he also scored in the final of the 2021-22 DFB-Pokal against Freiburg.
Ronaldo has allegedly told the 20-time English champions that he wants to leave Old Trafford this summer and is yet to return to pre-season training ahead of the club's tour of Thailand and Australia.
Man United have only made one summer acquisition so far, with left-back Tyrell Malacia joining from Feyenoord on a four-year contract earlier this month.