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Modric is a Madrid legend and still regularly starts in midfield alongside Toni Kroos and Casemiro at the age of 36.
The 2018 Ballon d'Or winner is in the final year of his contract and El Nacional report he isn't happy with new terms offered by Florentino Perez.
Modric feels 'undervalued' by the 'Los Blancos' hierarchy and believes he deserves a two-year extension for his years of service.
The Croatia international is even willing to take a pay cut to remain at the club after turning down an approach from Inter Milan in the summer.
He's frequently stated that Carlo Ancelotti, who returned to the Santiago Bernabeu dugout this summer, is his favourite manager to work under.
Real added teenage sensation Eduardo Camavinga to their squad this summer and Federico Valverde is battling hard for a regular place in the starting XI.
It means City could swoop in and bring Modric back to the Premier League on a free transfer.
Modric is keen to stay at the highest level so he can lead Croatia at the Qatar World Cup in December.
His first stint in England saw him become a fan favourite for Tottenham Hotspur between 2008 and 2012.
City have a number of options in midfield but Guardiola may want to fill the gap left by Phil Foden, who primarily plays as an attacker.
Bernardo Silva is also able to play out wide while club captain Fernandinho's contract is set to expire this summer.
Ferran Torres' departure for Barcelona means Gabriel Jesus is now the only recognised striker at the Etihad.
Despite that being a 'problem position' right now, City are ten points clear at the top of the league and Guardiola is happy to wait until the summer.
Last summer saw City attempt to sign Harry Kane but they refused to match Spurs' terms.
It's believed they'll try to sign Borussia Dortmund forward Erling Haaland as a high-priority target.
Do you think Manchester City need to sign another midfielder?
Let us know in the comments.