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Garcia,19, has been at the centre of interest from Barca throughout the summer after Pep Guardiola revealed that he did not want to sign a new contract at the Etihad Stadium, with his current deal running out at the end of the season.
There were some suggestions in Spain that he was left out of Monday night’s victory over Wolves to ensure he did not pick up a long-terminjury but those claims have been denied by the club.
Barca made former La Masia academy player Garcia a priority target in the summer but a €15 million (£14m/$18m) bid was rejected.
The Spanish club are now set to make another move before the transfer window closes on October 5 after selling Portuguese defenderNelson Semedo toWolves in a deal that could rise to €40m (£37m/$47m)with add-ons.
City are understood to value Garcia at around €35m (£32m/$42m) and are prepared to let him see outthe final 12 months of his contract unless they receive a suitable offer.
He is seen as a similar age and profile to new signing Ferran Torres, who joined formValenciain a package that could reach €36m (£33m/$43m) if all add-ons are matched.
Fellow centre-back Aymeric Laporte is also back training with the first-team squad after coming out of self-isolation following a positive COVID-19 test earlier this month.
The French defender could play a part against Bournemouth on Thursday night although Guardiola said he will play a number of youngsters.
City were without seven first-team players for the Premier League opener against Wolves and the Catalan wants to protect his players for Sunday’s visit of Leicester, who have won their two opening matches.
The club had hoped to have a new centre-back at the Etihad Stadium in for the weekend but are running out of time to close a deal.
Sevilla sporting director Monchi confirmed the Spanish club have turned down a bid for Jules Kounde, believed to be from City.