The Italian website reports that Blues co-owner Todd Boehly is “ready to double” the Nigerian international’s €4.5m (£4m) a year salary in order to secure his signature.
Osimhen has been in outstanding form this season, with his goal against Empoli at the weekend taking his total for the campaign to 21 in just 25 appearances.
His club are unlikely to let him leave on the cheap, though, with Calciomercato suggesting that Napoli president Aurelio De Laurentiis could hold out for a fee between €120m (£106m) and €130m (£115m).
Osimhen is also attracting interest from other Premier League clubs such as Manchester United and De Laurentiis will try to play off teams against each other to get the highest offer possible.
However, it appears Boehly is willing to blow Chelsea’s rivals out of the water for the striker, with the club’s transfer record expected to be smashed once again.