The former Monaco man has confirmed that talks are underway regarding a new contract with the French champions, where he has claimed he is "very happy" as he looks to pen an extension past 2022.
Mbappe continues to be linked with a move to the Spanish capital despite ongoing negotiations with PSG, although a recent report suggested that Real Madrid will now turn their attentions to Erling Braut Haaland.
However, AS claim that Real Madrid believe Mbappe's comments were more of a 'come-and-get-me' plea, and the Spanish champions are determined to offer the France international a more lucrative deal than PSG.
However, Real Madrid's considerable losses in the wake of the coronavirus pandemic could prove to be a stumbling block in their pursuit of the 22-year-old, and the club reportedly have to start repaying a £500m loan for Bernabeu renovations next year.
As a result, Zinedine Zidane's side would likely have to sell before they can lodge a bid for Mbappe, who leads the way in the Ligue 1 goalscoring charts with 14 strikes this term.