Cole is out of contract in six months and has yet to agree a new deal.
Ancelotti said: "He wants to stay and we want to keep him. We know the situation and we are talking with him. We are confident that Joe wants to stay. He's an important player for the squad and the fans. The fans like him and I think he will stay here.
"For Joe it's an important moment. He came back from the injury and he has an important appointment to achieve this season. The World Cup means it's important to play well for Chelsea. At this moment he has good mental attitude and good condition."
But Ancelotti insists Cole has more to give as the title race hots up.
The manager said: "He could do better. He must improve his confidence. I was out one year with injury, it's not easy to return. You need to have time to play and improve the confidence. It's not easy to come back and do the best immediately.
"He's very close. He played very well against Watford. Also the last game, maybe he met more difficulties playing in a new position.