In January, Deulofeu, 23, joined AC Milan on loan until the end of the season and his performances since arriving in Serie A have convinced Barcelona -- who hold the first option to buy him back when he returns to Everton at the end of the season -- to consider a move.
There are a host of other clubs lining up should Barca not exercise their right, though, and Parisi says Napoli may be one of them, even if a move there would be dependent on the future of reported Manchester United target Dries Mertens.
"Barcelona will give it some thought because they have the right to buy him back, but it will also be important what the lad wants," Parisi said. "[Napoli] could be an alternative if Mertens ends up on the market, but Deulofeu wants to be playing regularly and there would be a lot of competition for him there"
The Spain international has scored two goals and set up three more in 12 Serie A games since joining Milan, where he has been given a regular starting berth by Vincenzo Montella.