The Senegal international is proving to be one of the most in-demand players this summer and clubs from around Europe are keen to snap him up.
Both Arsenal and Chelsea have held talks with Napoli, while French champions Paris Saint-Germain are keeping tabs on the situation too.
However, according to Sportitalia, Everton are ready to blow the competition out of the water with a bid of of £46m.
The Toffees have money to spend this summer following the backing of billionaire investor Farhad Moshiri.
A new centre-back is high on manager Ronald Koeman’s list of targets and he could get his wish after Everton submitted their latest offer for Koulibaly.