The Gunners looked to be in the pole position and have even reportedly made a rejected bid in the region of €90m to Napoli for Osimhen's services.
However, it appears the Gunners will not get their transfer target this summer as Osimhen is not keen on leaving Diego Armando Maradona Stadium.
Osimhen wants to win the Scudetto with Napoli
The 23-year-old joined Napoli from Lille for a club and African record fee of €81.3m in 2020. Osimhen still has three years left on his contract, and he is not keen on leaving Naples this year.
The Super Eagles star was arguably Napoli's best player in the just-concluded Serie A season, scoring 14 goals in 27 games.
However, Napoli capitulated in the title race battle, which was eventually won by AC Milan. Still, Osimhen wants to stay at the club as he believes the Neapolitans have what it takes to win the Scudetto next year.
Also, with Lorenzo Insigne leaving, Osimhen will become the main man at the club and will have more responsibilities in the squad.
Osimhen's decision will come as a blow for Arsenal, who have identified the young Nigerian as a permanent replacement for Pierre Emerick-Aubameyang, who left for Barcelona in January.
It now remains to be seen if the Gunners will test Napoli and Osimhen's resolve by offering more money for his services.