Much has been made of Cole's contract negotiations in the last week and there was speculation talks had stalled - but Ancelotti is hopeful the player will be staying at Stamford Bridge.
His current deal expires at the end of the season but both club and player are continuing their dialogue.
"It's the same situation as last week," he added. "They are talking with the club. I think that Joe is very quiet, very calm and is training very well.
"He is improving his confidence and I think he'll do the second half of the season very well. It's important he signs. He's an important player - not only this year but in the future as well."