The World Cup winner can begin negotiations with clubs elsewhere from January, with talks over a new deal beyond 2022 failing to bear fruit.
Mbappe is widely expected to complete a free transfer to Real Madrid in the summer of 2022, but the France international has affirmed that he is still enjoying his time in Paris.
Speaking to reporters, Mbappe said: "I love to play. I love to play, I still love being on the pitch playing every game. So it's a pleasure to be able to play again today, to be able to help my team. I hope to continue for the matches that remain before the end of the calendar year.
"It's football! I always said that I had an incredible time at [Monaco]. I grew up there. I have had amazing memories. But now the page is turned. I play for PSG, I am very happy. I give everything I have for the club."
Mbappe's brace against former club Monaco at the weekend took him up to 100 Ligue 1 goals for Les Parisiens, with nine of them coming in 17 games this term.