The France star has long been linked with a move to Real Madrid but his current club continue to push for an extension
Paris Saint-Germain sporting director Leonardo has revealed the club is making progress as they look to tie Kylian Mbappe down to a new deal.
The 21-year-old's current contract expires in 2022 with PSG eager to secure an extension to ward off interest from the likes of Real Madrid and Barcelona.
While there was some doubt over whether Mbappe would remain in Paris , the Ligue 1 giants are making headway with their star attacker as talks continue heading into the new year.
"We're talking. We want to discuss, and he also wants to discuss. Now is also the time to come to a clearer idea of his future," Leonardo told Canal+ on Saturday.
"It is going well. We have taken steps forward compared to 10, 15 days ago and we will continue."
On the pitch, Mbappe is without a goal in his past three appearances for PSG , failing to score from any of his nine shots in those games and hitting the target only twice.
The 2018 World Cup winner has also now gone nine games without a goal in the Champions League, though his manager Thomas Tuchel isn't concerned.
"We will have to decide on that today. In my head there are several different possibilities," Tuchel said on Friday.
"We have to make decisions for Tuesday as well. We may have some changes to make, but for Kylian personally, I am calm.
"For me he had a good game [against United], a better game than in matches he has scored in. He put in a lot of effort both in an attacking and defensive sense. He had a bit of bad luck with his chance, but it will come for him. He should stay calm because I am also very calm."
Ex-Real Madrid president Ramon Calderon has recently urged his former club to sign Mbappe next summer with Los Blancos seemingly in need of an attacking spark.
"Without a doubt, Mbappe is the player most desired by all and it would be great news for our team," Calderon told Goal .
"He is a player who, being very young, has already managed to attract the attention of all the fans and presumably his best moment is yet to come.
"What the big clubs always need is to have the best players in their primes, regardless of their age."