The Portuguese left Los Blancos for Juventus in a shock move of £ 99m earlier this week.
And that left Real looking for options to replace Ronaldo.
The Spanish distributor Diario Gol, known for his bold and extravagant transfer requests, says an offer has been made for Mbappe in the last 24 hours.
The 19-year-old French star impressed France at the World Cup this summer and has a chance of glory this afternoon against Croatia. It is known that Madrid wants Kylian Mbappe to move to Spain to replace Ronaldo.
And reports from Spain claim Real Madrid have made an offer of £ 88m (€ 100m) for Mbappe which includes Casemiro as part of an exchange deal.
Paris St-Germain would also be interested in taking Isco or Marco Asensio as part of the deal.
But Real Madrid is determined to keep both stars this summer.
New manager Julen Lopetegui has also been associated with Neymar and Chelsea, striker Eden Hazard, to replace Ronaldo.
Diario Gol claims that Real Madrid’s big-big Florentino Perez has now Mbappe ahead of Neymar on his wish list.
This is following his impressive displays for France in Russia at the World Cup.
Los Blancos would not be convinced that Hazard would score enough goals to replace Ronaldo.
Mbappe hopes to make another statement this afternoon as France face Croatia in the World Cup final.
Starsport will bring you all the action from the kickoff of 16h.