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.
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