The Croatia creator has been told he will play an important role by both English giants, according to reports.
Kovacic, 24, has spent the majority of his Los Blancos career stuck behind the likes of Toni Kroos, compatriot Luka Modric and Casemiro in the midfield pecking order – making 109 appearances in three seasons since moving from Inter Milan in the summer of 2015.
Kovacic has featured 73 times for the Spanish behemoths in La Liga during that time – but only 37 of those have been starts – and he revealed before the World Cup that he was keen to quit the Bernabeu.
Spanish newspaper Marca claim United and Liverpool have both made promises to Kovacic, who helped his side reach the final in Russia.
Kovacic hinted at a move away back in June, saying: “I would like to play more in Madrid because I love football and being on the pitch, and I know that it’s difficult to play in Madrid.
“Especially because I was very young, I understand the situation, but for that reason I think the best for me it is that I go to another club where I have the opportunity to play regularly as a starter.
“It’s an opportunity that I think I can have and that I want right now.”
The player has supposedly told new Real boss Julen Lopetegui he is keen to quit the club this summer, although the new man could grant him his wish of more playing time as the former Spain coach looks to shake things up following his arrival and the departure of Cristiano Ronaldo to Juventus.
Marca add, though, that United and Liverpool are not alone in pursuing Kovacic. Bayern Munich and the Bianconeri would also both love to snap him up.
And Pep Guardiola would also welcome him at Manchester City, with Real slapping a £50million price tag on Kovacic.
New Real Madrid signing Vinicius Junior has revealed that Neymar is his “idol”.
The 18-year-old moved from Flamengo for a fee of €45 million and says he would love to play alongside his fellow Brazilian at some point in his career.
Watch the video below for Vinicius’ quotes.
Real Madrid have kicked off their preseason preparations but several of their World Cup stars are still on holiday.
Brazilian left-back Marcelo is among those players currently enjoying their breaks and but football is still very much a part of his vacation.
The defender uploaded a clip onto his Instagram of him participating in bit of footvolley with some friends.
The footage was taken on Ipanema Beach in Rio.