Mbappe signed a new contract with PSG at the end of last season that will keep him at the Qatar-owned club until 2025, though French media reports indicate that the final year of the contract is optional and up to the player.
This increases the chances of the 24-year-old being able to leave for free at the end of next season.
Mbappe’s comments come a week after he complained over the club’s use of an interview with him as part of their season-ticket advertising campaign, before the club removed the footage.
He joined PSG in 2017 from Monaco and still hopes to win the Champions League with his home city club.
“I have already got to one final and a semi-final. I have been to the quarter-finals, the last 16. I have done everything but win it,” he said.
“That is all I am lacking. I hope it will come as soon as possible.”
A World Cup winner with France in 2018 and runner-up last year, Mbappe said it was his “dream” to represent his country at the Paris Olympics.
“I hope to be there. Everyone knows I have always dreamed of playing at the Olympic Games but it doesn’t depend on me,” he admitted.
Clubs are not usually obliged to release players to compete at the Olympics as it is not part of the FIFA international match calendar.
Mbappe added: “I won’t force it because if people don’t want me to play at the Olympics that means I must not.”
“The truth is that it is not part of the FIFA calendar. I have to think about my club, and my national team too because there is the Euro just before it, so it needs to be discussed.
“All these things need to be considered but of course it would be a dream to play at the Olympics, all the more so in Paris.”