Madrid signed Areola on loan from Paris Saint-Germain late in the transfer window, with Keylor Navas moving to the Ligue 1 champions from the Santiago Bernabeu.
Mbappe, Areola's team-mate at PSG for the past two seasons, has long been linked with a switch to Los Blancos, while Manchester United star Pogba is also a reported target.
Both Mbappe and Pogba missed France's recent Euro 2020 qualifiers against Albania and Andorra through injury, though that did not stop the press quizzing Areola on the future of his compatriots.
"The thing I've spoken to Kylian about is his injury, he has to get back as quickly as possible from that and we'll see what happens in the future," Areola told a news conference.
"I can't go into detail if we've spoken about Madrid or not. I'm here and I want to be part of the history of this club.
"He's at Paris at the moment, he needs to recover from his injury, get his level back. Everyone has their own way forward, their own story and we'll see what happens at the end of the season.
"I have not spoken to Paul. He was injured in the last time we met with the national team, but I know him well. He's a great person, a great player with great quality.
"But everyone has their own way and their own road, so we'll see what happens."
Mbappe's injury means he is set to miss PSG's Champions League meeting with Madrid on September 18, a fixture Areola is relishing.
"It's great coincidence that we play PSG, I'm going to go back to the club very quickly," Areola said.
"[Madrid's players] haven't spoken about that yet, about how they're going to play.
"For me it's about getting involved in the squad and being comfortable here, I am very happy to have trained now we've got a game, it's an important one against Levante and we have to prove that we're ready."