Florentino has spent relatively little in this summer's transfer market, but does have the cash power available to bring World Cup winner Mbappe to Spain before the market shuts at the end of the month.
AS says the key day will be Monday, when PSG must pay €180m to AS Monaco for the striker after last season's 12 month loan. It's suggested PSG may be forced to give Mbappe back to ASM as such an outlay will see them break UEFA's Financial Fair Play laws.
With the Premier League and Serie A markets now closed, it will leave Real with a clear run at signing Mbappe should he be sent back to ASM.
Just today, LaLiga president Javier Tebas confirmed UEFA were still investigating PSG over their recent transfer spending.