The Brazilian was linked with a move to Goodison Park in January as well but the move never materialised.
Allan has fallen out of favour at the Italian club since then and Ancelotti is prepared to offer him an escape route.
It will be interesting to see if Ancelotti succeeds in signing the midfielder this time.
He was a key player for Napoli when Ancelotti was in charge and the Italian could bring the best out of him at Everton once again.
Everton need a midfield controller to dominate games and Allan would be ideal. He has proven his quality in Serie A and in the European competitions against top-class opposition.
The Brazilian is at the peak of his powers right now and he could make an immediate impact if the transfer goes through.
This would be the type of signing that takes Everton onto the next level.
Apparently, the Toffees might have to pay around €40m to sign the 29-year-old midfielder this summer.