The Brazil international has found himself out of favour at the Stadio San Paolo under Gennaro Gattuso, with Napoli looking to cash in on him.
It has led to Tuttosport reporting that former Napoli coach Carlo Ancelotti is keen to bring Allan to Goodison Park, but faces competition from fellow Premier League outfit Wolves.
The 29-year-old was linked with a move to Paris Saint-Germain in January, but a switch failed to materialise. However, it appears that the strongest interest in the former Udinese and Vasco da Gama midfielder has come from England.
Allan has scored 10 goals in 208 appearances since joining the Partenopei in 2015, and has helped the club to the Coppa Italia last month.
Despite being eligible to represent the Italian national team, Allan committed himself to his country of birth in 2019 and lifted the Copa America with Brazil last summer.