Mbappe has recovered, but Real Madrid will take no risks for clash vs Lille
The France captain, who joined the Spanish side from Ligue 1 champions Paris St Germain on a free transfer in June, picked up the problem during Madrid's 3-2 home win over Deportivo Alaves in LaLiga last week.
He has since missed one game - a 1-1 LaLiga draw at Madrid's bitter rivals Atletico Madrid on Sunday.
"Mbappe has recovered very well, very quickly," Ancelotti told reporters ahead of Wednesday's game at the Stade Pierre-Mauroy.
"He trained yesterday and today, he will do the full training session with us. Then we'll make the decision together because the last thing we want to do is take risks.
"Mbappe has had an overload and in less than a week he has recovered well.
"He wanted to travel to play. We'll see what training he does today. If he's at full strength, he can play. If there is no risk, he will play from the first minute."
Madrid are second in LaLiga, three points behind rivals Barcelona after eight matches. But Ancelotti said there was room for improvement, especially when they face Lille, who sit fifth in Ligue 1.
"We have to get points, taking into account the value of the opponent. They are a team that plays very well. They like to play with the ball, they have young players with quality," the Italian said.
"Every match has to be fought. That's why we're here. We are doing well. We are convinced we can improve. We are ready. There are a lot of games, but we are pretty good."
Ancelotti was also asked about the heated Madrid derby. On Monday, Atletico permanently banned a fan for throwing an object onto the pitch during the game at the Metropolitano Stadium.
The derby was suspended for just over 20 minutes after home fans hurled objects onto the pitch as the visitors celebrated the opening goal.
"The point is that violent people are not allowed in football. Not at Atletico, but on any pitch. Football doesn't need them," Ancelotti said.
"Let them stay somewhere else, somewhere that is not dangerous. I'm talking in general. Whether it's a violent person from Madrid, Barca, Atleti, Villarreal, it doesn't matter. Let the violent ones leave us in peace."