Osimhen has been linked with the Premier League trio, who are keen to bolster their attacking options at the end of the season.
Newcastle United reportedly tabled an offer for the Nigeria international in January which was rejected by Napoli.
La Gazzetta dello Sport, as cited by The Express, say that Osimhen would be prepared to join the Gunners over both United and Newcastle, who are both also said to be interested in a deal.
Arsenal are desperate to sign a new striker with Eddie Nketiah and Alexander Lacazette set become free agents this summer.
The Gunners will however need to pay at least €100m to sign Osimhen, who still has three-and-a-half years left on his contract with Napoli.
The 23-year-old has scored 17 goals in 29 outings so far this season for the Partenopei.
Arsenal are likely to finish in top four in the Premier League this season, which will also play a key role in bring Osimhen to the Emirates Stadium.
Transfer guru Gianluca Di Marzio recently stated that any club interested in Osimhen will have to pay at least €100m (£83.7million) in order to secure his signature.
“I don’t think he will be sold for €80million (£68.6million) because he was bought for €70million (£60million). So, I think that (Aurelio) De Laurentiis is very smart to buy and very difficult when he has to sell the players. I don’t think he will let Osimhen go for less than €100million (£83.7million) – minimum. So, it depends on which club in Premier League will have all this money to spend in the market only for one player,” Di Marzio told wettfreunde.
Osimhen linked up with Napoli from French Ligue 1 outfit Lille two seasons ago, after an impressive debut campaign for the club.