But Partenopei president Aurelio De Laurentiis has told Madrid they will have to lower their demands for the attacker, who is surplus to requirements at the Santiago Bernabeu.
De Laurentiis is confident a deal can be struck, however, having already claimed that the player wants to make the move to play under his old boss once more.
Ancelotti is also keen and has already been in contact with the playmaker, though he doesn’t see his side as being desperate for the signing as the new season approaches.
"James can play in many positions behind the centre-forward," Ancelotti told TV Luna on Saturday after a pre-season loss to Benevento. "He is a number 10 used to playing behind the striker or as a winger, with the tendency to cut inside.
"I sent him a happy birthday message this week.
"There are negotiations in progress. It's going to take a very long time, but we aren't desperate or anything.
"If it doesn't work out, we'll still be a strong team and might go for a different target."
Napoli have also been linked with Mauro Icardi, who has been told he can leave Inter, but Ancelotti indicated he is satisfied with options in attack that include Lorenzo Insigne and Dries Mertens.
"As for the striker, a modern centre-forward can't just be a finisher now, which is why Arkadiusz Milik is very important for us," the Italian said.
But the club did earn second spot in the table and have Champions League football to look forward to again next season.