The French forward's contract with the reigning Ligue 1 champions is set to expire in 2022 but previous reports have claimed that the player is not keen on extending his current deal.
As a result, PSG might need to cash in on the 2018 FIFA World Cup winner next year rather than risk potentially losing him for nothing in two years' time.
While there could be a bidding war for Mbappe should he become available, Bundesliga giants Bayern have ruled themselves out of the running for his services.
"I love Mbappe and his way of playing, but we will never be able to bring him to Bayern," club CEO Rummenigge told Le Figaro.
"Anyway, he is where he is. Nasser [Al-Khelaifi, PSG president] is a good friend of mine. I will not bother him on this subject."
Since joining PSG from AS Monaco in 2017, Mbappe has registered an impressive 103 goals and 59 assists in 140 appearances across all competitions.