The Italian spent 18 months in the southern Italian city before joining the Toffees in December.
And CalcioMercato says Ancelotti is keen to bring Allan to Goodison Park.
The Brazilian midfielder has long been of interest to Manchester City.
It would take a serious offer to sign the 29-year-old, who is not out of contract until 2023.
But Ancelotti is confident Everton can strike a deal.