PSG have tabled Kylian Mbappe a new four-year contract.
RMC says Mbappe has received a 4-year extension offer from Paris Saint-Germain.
PSG made the offer to the forward several months ago.
The report says the 22-year-old World Cup winner is still thinking about it and is yet to give the Ligue 1 champions an answer.
Mbappe has been continually linked with Liverpool and Real Madrid, and RMC claim if Mbappe does not sign a new deal, then PSG will consider making a move for Lionel Messi on a free transfer.
