The Napoli star, 25, is set to be on the market with his contract possessing a release clause worth around £94million.
Man Utd are set for a big summer ahead, following the arrival of Sir Jim Ratcliffe as partial owner.
The Red Devils are eager to become more “forward thinking” with their transfer strategy.
According to the Independent, Osimhen will be seen as an ideal signing by United chiefs due to his age and adaptability.
Should the Red Devils bring the Nigerian to Old Trafford, Osimhen will provide a different option to Rasmus Hojlund up top, where United currently lack depth.
Anthony Martial is set to leave on a free transfer, while Marcus Rashford feels more at home on the left flank.
Osimhen is set to have two years remaining on his Napoli contract come the summer.
In order to secure his signature, the Red Devils will have to beat off fierce competition.
Premier League rivals Chelsea and Arsenal are both keen on the former Lille striker.
While Paris Saint-Germain are also set to be a key player, following the near certain exit of Kylian Mbappe to Real Madrid.
Already planning for life after Mbappe, PSG chiefs want to place a new emphasis on developing young talent, moving away from their previous glitzy strategy which has ultimately been unsuccessful in Europe.
With Mbappe set to leave a huge gap upfront, however, the French champions could make an exception to their new rule in order to splash out on Osimhen.
The forward has Ligue 1 experience, scoring 18 goals in 38 games for Lille during the 2019-20 season.
He subsequently joined Napoli, going on to net 72 goals in 123 appearances thus far – helping them win the Serie A title last term.
This time around he has 11 goals in 16 league outings, having battled with a hamstring injury before missing seven games while at Afcon.
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