Osimhen's name first arose during Arsenal's talks with Galatasaray over the Turkish club's interest in Ethan Nwaneri and Gabriel Martinelli, with Chelsea and Tottenham also previously credited with interest in the striker.
While Martinelli ultimately rejected the chance to move to Istanbul, Osimhen was more measured when asked directly about the rumours linking him with a switch to the Emirates Stadium.
"There are always rumours in transfer seasons," he said. "I will take care of my business.
"I am focused on my job, then we will see and think further."
Arsenal are reportedly considering a move for the forward, who is valued at around £58m, though it remains just one of several attacking options under consideration following a difficult summer in the market.
The club have already seen pursuits of Morgan Rogers and Julián Álvarez complicate their search — Rogers opted to join Chelsea, while Atlético Madrid have held out for a fee in excess of £100m for Álvarez — and missed out on Real Madrid's Vinícius Júnior earlier in the window too.
Osimhen has made no secret in the past of wanting to test himself in the Premier League.
Speaking in 2023 after being named Best Foreign Athlete of the Year by the Italian Foreign Press Association, during a spell of outstanding form that fired Napoli to the Serie A title, he said: "I think playing in one of the top five leagues in the world is an amazing feeling for me. A lot of people worldwide consider the Premier League as the best and the strongest league, but now I'm in one of the best leagues in the world, which is the Italian Serie A.
"I'm working so hard to make sure that I achieve my dream of playing in the Premier League some day, but like I said, it's a process and I just want to keep on this momentum and continue to do well."
Arsenal currently have Viktor Gyökeres leading their attack, with Kai Havertz and Gabriel Jesus as alternatives, while midfielder Mikel Merino has also been used as an emergency striker by Mikel Arteta in the past. Any move for Osimhen would add further competition to that department as the champions look to defend their title.