A move during this summer's transfer window could be difficult due to the coronavirus outbreak, but it would certainly not be a shock to see the 21-year-old complete a switch to the Bernabeu.
Indeed, Mbappe only has two years left to run on his contract with the French champions and would see his value plummet if he does not pen a new deal ahead of next summer's window.
The France international has again been in terrific form for Thomas Tuchel's side during the 2019-20 campaign, scoring 30 times and contributing 17 assists in 33 appearances in all competitions.
Here, Sports Mole looks at the shirt numbers available for Mbappe at the Bernabeu should he arrive before the end of this summer's transfer window.
Mbappe was presented with the number 29 shirt upon his arrival at PSG from Monaco, but the France international currently wears '7' for the Ligue 1 champions.
Eden Hazard was handed the number seven shirt at the Bernabeu upon his arrival from Chelsea last summer, though, and it would be very surprising to see the jersey taken off him.
Mbappe currently sports the number 10 for France, meanwhile, but that shirt is occupied by Luka Modric at Madrid. The 34-year-old is coming to the end of his career, though, and it would not be a shock to see the Croatian relinquish control of the number or indeed have it taken off him.
Madrid's numbers are actually filled from 1-18, with '19' the lowest available at this moment; Alvaro Odriozola sported that number in the first half of the campaign before joining Bayern Munich on loan. The '26' is also vacant at this particular moment but otherwise there are no real openings.
It seems unlikely that Mbappe would agree to join Los Blancos without the promise of taking on his preferred number, though, and that situation could be solved by removing Modric from the '10'.
In terms of the top 20, the number 17 could also be available with Lucas Vazquez being tipped to depart, although Mbappe would surely want one of the so-called glamorous shirts.
The number 11 jersey would surely be enticing for the 2018 World Cup winner, but it is difficult to look past 'Mbappe 10' at the Bernabeu next term should the move go through in this summer's transfer window.