Kovacic is currently on holiday after helping Croatia to the final of the World Cup and will hold talks with new Los Blancos boss Julen Lopetegui upon his return.
The Madrid midfielder has a contract at the Bernabeu until 2021 but having failed to impress under Zinedine Zidane last season – making just 10 La Liga starts – he is exploring his options.
Spanish publication OK Diario claim he is already in talks with City over a potential transfer though.
News of this has not sat well with Madrid chiefs who are adamant he won’t be sold as he is needed to help the club challenge Barcelona for honours next season.
But the 24-year-old doesn’t appear to be prepared to wait until he hold talks with Lopetegui to seek assurances over his future, with Pep Guardiola keen on bringing him to the Etihad.
A host of other clubs are also interested in his services, with Manchester United, Liverpool and Bayern Munich keen to offer him more playing time.
Madrid do not entertain the idea of selling the midfielder but that has not stopped other clubs making enquiries.
OK Diario claim the likes of Liverpool, Arsenal, Inter Milan and Juventus have all submitted proposals to take him away from the Bernabeu.
They are all aware of the Kovacic’s situation in the capital and are hoping to take advantage by offering him a way out.
However, Madrid’s stance remains clear and any potential suitors have been told to look elsewhere.
Liverpool have already acquired Naby Keita and Fabinho in midfield this summer but Jurgen Klopp is thought to be on the lookout for any late attacking options to add quality in depth.
Meanwhile, Arsenal boss Unai Emery remains in the market for an attacking midfielder with Barcelona’s Ousmane Dembele an option, along with Kovacic.
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.