Brazil international Allan is set to finally depart Napoli in a reported £25million (€27.9m) deal after repeated talk of a move away from the Serie A club in recent years.
A €100m transfer to Paris Saint-Germain was mooted in 2019 when Carlo Ancelotti was in charge of the Partenopei.
But Allan is instead now heading to Merseyside to link up with Ancelotti again at Goodison Park, De Laurentiis says.
He told Radio Kiss Kiss: "We are at the final greetings. Allan will go to Everton."
Allan, 29, joined Napoli from Udinese in 2015 and has since made over 150 Serie A appearances for the club, also winning the Coppa Italia last season.