Toffees boss Rafael Benitez wants to add another centre-back to the ranks at Goodison Park and the club have been linked with Koulibaly, who played under the Spaniard at Napoli.
Now Everton have made their move, according to Italian outlet Calciomercato.com, with an offer put in for the Senegal international.
It is though claimed to be too low and Everton are expected to go back in with a new offer soon.
The Italian side have been open to selling Koulibaly in recent transfer windows, but no club have offered a sum they deem acceptable for a player widely considered to be one of the top centre-backs in world football.
Napoli have Koulibaly under contract until the summer of 2023.
At the age of 30, this summer could be the Azzurri’s best hope of earning a substantial fee for the defender, who will enter the final 12 months of his contract next summer.
Koulibaly joined Napoli in 2014 when Benitez was at the helm and played regularly under the Spaniard.