Paris Saint-Germain are believed to have placed Mbappe on the transfer list, with the French giants determined not to lose their star attacker on a free transfer next summer.
The Paris outfit allegedly believe that the France international has already come to an agreement with Los Blancos over a move next year, but they are hoping to sell him in a big-money deal in the current window.
Real Madrid have made four signings this summer, with Jude Bellingham, Arda Guler and Fran Garcia arriving on permanent deals, while Joselu has made the switch on loan from Espanyol.
Brahim Diaz is also back at the club following a loan spell at AC Milan, but Karim Benzema, Marco Asensio, Eden Hazard and Mariano Diaz are among those to have moved on.
Despite an apparent lack of options in the final third of the field, Ancelotti has said that his squad for the coming season is "complete", with the Italian confident in the players available to him.
"I think we are complete. The new players are doing very well. Brahim and Joselu have shown that they can contribute to the team offensively. I think the team has a lot of attacking options to give us chances to score goals," Ancelotti told reporters ahead of Saturday's pre-season friendly with Barcelona.
When questioned on Mbappe later in the press conference, the head coach said: "It doesn't bother me when you ask me about him, but I'm not going to answer."
Real Madrid have now won both of their pre-season games this summer, recording a 3-2 victory over AC Milan in their opener before beating Manchester United 2-0 last time out.
"In the two previous games we've played some good football and we also have some things to improve on. It's an opportunity to get the motor warmed up," he added.
"We're doing well and we want to continue in the same vein. We'll do our best, but we're playing against a very strong opponent with a lot of quality. The result is the least important thing; the most important thing is to keep progressing. It's a very demanding test because the opponents are very strong.
"We did well against Manchester United and we have to be consistent. It's too early to assess what we're going to do. We're doing well, but then comes the season and we need to have continuity, commitment, and attitude in every match."
Number one goalkeeper Thibaut Courtois is set to make his return from injury for Real Madrid against Barcelona, but summer arrival Guler remains unavailable for selection due to a leg issue.