The veteran left back has played more than 400 games for the Toffees, and he is now thinking about the rest of his career.
At 35, he wants to contemplate his next move.
But Ancelotti hopes that Baines, who played in the second half against Norwich in a 1-0 win in midweek, will stay for at least another season.
He told reporters after the game: "I hope not [Baines leaving]. I think the situation with Leighton is clear.
"Every one of us, the club, myself, the team-mates, want Leighton to stay another season.
"We are awaiting his answer and we hope the answer is 'yes'."