The Blues were linked to the Nigerian forward throughout the summer window.
However, a move did not materialize, with Osimhen going to Galatasaray on loan instead.
According to Corrierre dello Sport, Osimhen remains eager to go to the Premier League.
Whether a deal can be done between Chelsea and Napoli is not yet clear.
However, there is a clear will from the player to get a move to Stamford Bridge.