The Nigerian has become one of the most sought after forwards in world football after 21 goals in 44 league appearances for Napoli.
Gunners boss Mikel Arteta is targeting a big striker signing this summer after the departure of Pierre-Emerick Aubameyang.
Alexandre Lacazette and Eddie Nkeitah are also entering the final months of their respective contracts.
Gazzetta dello Sport - via Sport Witness - have reported that Osimhen is on Arsenal's radar.
However, their pursuit of Osimhen will depend on whether they have enough to cash to meet Napoli's asking price of £84million.
The north London club are currently in fourth on the Premier League and securing Champions League football could go a long way to signing Osimhen next summer.
Manchester United and Newcastle United have also been linked with the 23-year-old.
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