The 23-year-old has enjoyed a prolific 2021-22 campaign in front of goal for the Italian outfit, scoring 18 times and providing six assists in 31 appearances across all competitions.
According to Corriere dello Sport, via the Daily Mirror, the Red Devils have identified the Nigeria international as one of their main attacking targets this summer and have decided to approach the player regarding a possible a switch to Old Trafford.
Osimhen has recently hinted that he could stay at Napoli, after stating to the media that he hopes to work under head coach Luciano Spalletti for "many more years".
The striker is, however, believed to be interested by the prospect of playing in the Premier League, with United set to face competition from the likes of Arsenal and Newcastle United for the player's signature.
Osimhen, who is valued by Napoli at around £100m, is under contract with the Serie A club until June 2025.