Mbappe landed in the Spanish capital last week to start training with the team after he had joined Real as a free agent on a five-year deal in June, ending a transfer saga that rumbled on for years.
"Mbappe has arrived well, just like the other players who joined last week," Ancelotti told a press conference on Tuesday.
"We haven't had much time to train but we are doing very well, and Kylian has also arrived in good shape. He is adapting very well. Obviously, everyone who is here can play tomorrow."
The Italian coach had previously said following one of the recent US friendlies that it is the players who won the Champions League who should play the Super Cup.
Ancelotti, however, did not rule out the Frenchman making an appearance at some stage.
Asked whether Mbappe could be assigned penalty-taking duties, the manager said that the job would only be given to a player who started the game.
"Mbappe is a penalty taker, he does it very well," Ancelotti said. "(But) (Jude) Bellingham has done well in the European Championship, and (Federico) Valverde was spectacular in Copa America.
"So we have a lot of penalty takers. I have to pick one of them for tomorrow's game. Obviously, I have to pick one that will start the game."
Real, who have clinched five Super Cups so far, have a chance to become the standalone leaders of the competition ahead of Barcelona and AC Milan, who have also won five times.
They could also make history this season if they kick-start their campaign with a win, as there will be seven titles up for grabs for the very first time thanks to FIFA's new Intercontinental Cup.
"As always, we're starting the season with all the excitement and desire," Ancelotti added.
"It's the first title of a season that is going to be very demanding but can also be very successful. We want to start it well. We are aware of the difficulties but I see the team in good shape, motivated to play a great game."
