The 18-year-old is one of the most in-demand players in world football after a sensational campaign, where he scored 15 league goals and became the youngest scorer in a Champions League semi-final.
PSG have reportedly held face-to-face talks with the teenager and Real have made him a priority signing, while Arsene Wenger had hoped to persuade him to join Arsenal.
But with Monaco likely to hold out for a fee in excess of €150 million (£132m), any clubs wanting to sign Mbappe will need to break the bank.
And, according to the Evening Standard, that has prompted Real to listen to offers for Kovacic, who was restricted to just 19 league starts last season and is itching for more game time.
He could fall even further down the Bernabeu pecking order if the club successfully snap up Real Betis midfielder Dani Ceballos, who is close to completing a move to the Spanish capital for a bargain price.
The potential sale of Kovacic would add valuable funds to Real’s Mbappe transfer kitty, especially with Alvaro Morata and James Rodriguez still at the club.
Kylian Mbappe's Ligue 1 stats 2016/17Games played29Goals15Assists8
Real could have fetched a handsome sum for the duo, but United pulled the plug on negotiations for Morata when they landed Romelu Lukaku and president Florentino Perez has said the club have not received any offers for the pair.
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Tottenham, meanwhile, could face a battle to sign Kovacic, with Real also offering the 23-year-old to other clubs around Europe as they try to get him off their books.
Their hopes of signing the Croatian could be knocked back by his wage demands, with Kovacic currently earning more than Spurs’ rigid wage structure would allow them to offer.