Mbappe has been heavily linked with a move to LaLiga giants Real Madrid, where head coach and fellow Frenchman Zinedine Zidane has made no secret of his admiration for the 21-year-old star.
PSG sporting director Leonardo has previously revealed talks over a new contract are progressing, with Mbappe's current deal running through to the end of the 2021-22 season.
Asked about his future following PSG's 6-1 Coupe de la Ligue quarter-final rout of Saint-Etienne on Wednesday, Mbappe told reporters: "I am ready to play football first. Because we are in January.
"We start the final sprint, where we can compete for trophies. I think it's not the right time to make some waves.
"The club are calm, serene, everyone is walking in the same direction so talking about external things of the pitch would not be realistic or good."
Mbappe was on target against 10-man Saint-Etienne as PSG cruised into the semi-finals thanks to Mauro Icardi's hat-trick midweek.
PSG led 3-0 at half-time via Icardi, Neymar and a Jessy Moulin own goal, and the hosts maintained their dominance in the second 45 minutes.
Mbappe helped Icardi complete his hat-trick with a pair of assists before the latter returned the favour by setting up the Frenchman in the 67th minute – Saint-Etienne's Yohan Cabaye bagged a consolation four minutes later.
On the relationship between Mbappe and Icardi, who is on loan from Serie A outfit Inter, PSG head coach Thomas Tuchel said: "I don't know if they reach another level but I know they love to play together.
"They play all four with great complicity especially Kylian and Mauro. It's obvious and it's necessary. If you play with four strikers, it's necessary that they try to find themselves on the pitch. They try to put each other in the best conditions. They give the ball to make an assist or to find a guy in a better position.
"They did great tonight. We speak a lot about the four strikers but you know that for me it's all about the team, we need to play as a team with the eleven players. That's football."