The La Liga side were reportedly willing to fork out a nine-figure sum to sign Mbappe over the summer, but PSG stalled over a bid and the forward remained in his homeland.
Mbappe has since confirmed that he asked to leave PSG over the summer amid interest from Real, and he is widely expected to complete a free transfer to the Bernabeu next summer.
However, Perez has hinted that a deal could be on the card sooner, telling El Debate: "In January we will have news from Mbappe. We hope that on January 1 everything can be solved."
The Real chief claimed that his words were taken out of context not long after, though, subsequently telling RMC: "My words were misinterpreted. What I said is that we have to wait until next year to hear from you, always with respect for PSG with which we have good relations."
Mbappe boasts four goals and five assists from 11 appearances across all competitions in the 2021-22 campaign so far and also recently admitted to referring to Neymar as a "bum" in a recent Ligue 1 game. body check tags ::