Neymar, who has been heavily linked with a return to Barcelona in recent weeks, is known to have been a target of Real for well over a decade, going right back to his formative years when he was invited over from Brazil to visit the club when he was just 13.
With little genuine movement in the ongoing Barcelona saga, the Catalan press earlier this week stirred up gossip about Los Blancos at last reigniting their interest.
Now, however, just days later, AS claims to have learned that Real have 'definitively decided against signing Neymar', seeing the 27-year-old as 'too risky an investment'. The implication is that he is off Real's transfer radar for good.
It is said there has been 'no contact' and there will be 'no direct or indirect offer'.
Currently at war with PSG for missing the start of pre-season training - he and his camp claim it was for a pre-arranged charity commitment - off-field issues have begun to blight Neymar's career and AS hints they are at least part of the reason for switching to Mbappe.
The report describes the Neymar 'entourage' as 'an unwelcome addition to any potential transfer', before going on to highlight Mbappe's 'clean-cut image', as well as the youngster's immense marketing potential and obvious on-field ability.
But with Real having already made one 'Galactico' signing this summer after sealing the arrival of Eden Hazard from Chelsea, the suggestion is that any approach for Mbappe will be delayed until next year.
PSG sporting director Leonardo gave hope to possible Mbappe suitors this week when he refused to promise that the 2018 World Cup winner will sign a new contract in the French capital. His current deal runs out in 2022 and by next summer he will be into the final two years of his deal.