Madrid has pursued Mbappe since he moved to PSG from Monaco in 2017. His contract runs out next summer and he has so far rejected three bids by the club to extend his deal beyond 2022.
PSG, who have yet to field Mbappe alongside Neymar and Lionel Messi, have rejected the opening bid.
But they have been offered Ronaldo as a replacement and have also been urged by Neymar to consider his international teammate, the Everton striker Richarlison, as Mbappe’s replacement.
Questions will be asked as to how Real Madrid can afford Mbappe after 300m euros was wiped off the club’s revenue by the coronavirus pandemic.
The squad accepted a 15 per cent wage cut last season and several players this season have already negotiated new contracts that will enable the club to pay them over a longer period of time.
Madrid president Florentino Perez’s fronting up of the doomed European Super League project was seen as an indication of the club’s desperate financial state. He declared that football would be dead by 2023 if the Super League was not permitted.
Madrid made no signings last summer and have so far signed only David Alaba on a free transfer from Bayern Munich while selling Martin Odegaard to Arsenal and Raphael Varane to Manchester United.
French radio station RMC reported on Monday night that PSG was now open to allowing Mbappe to leave with one year left of his contract.
But Madrid was originally sceptical of the supposed softening of the Ligue 1 club’s stance. Last night’s dramatic bid will publicly test the Qatari-owned club’s resolve.