The 27-year-old has entered the final year of his contract at Camp Nou and appears likely to stay for the 2020-21 campaign
Garcia has been subject to strong interest from Barcelona, where he came up through the youth ranks before moving to City in 2017.
Pep Guardiola revealed in August that Garcia did not want to sign a new contract at the Etihad Stadium, with his current deal running out at the end of the season.
“He has one more year and after that, he doesn’t want to extend. We want it but he doesn’t want to extend it so I imagine he wants to play in other places,” Guardiola said.
Rafinha is another player whose contract is set to expire at the end of the 2020-21 campaign, and the 27-year-old’s future is up in the air after taking in loan spells at Inter and Celta Vigo in recent seasons.
Reports have mentioned Rafinha’s name in a possible swap deal involving Garcia, but sources tell Goal that the midfielder has not been told anything about a move to the Etihad.
One year ago, Rafinha and Barcelona agreed that the Blaugrana would allow him to depart should they receive a bid of €16 million (£15m/$19m).
Though there has been interest from several clubs in Rafinha’s services, none of the offers have come close to that amount as interested sides remain hamstrung by financial limitations stemming from the coronavirus crisis.
Celta Vigo are one of the interested teams after Rafinha made 29 La Liga appearances for them on loan last season, scoring four goals.
With Barcelona unwilling to lower their €16m asking price, Rafinha has accepted that he may be forced to stay at Camp Nou this season and play out the remainder of his contract before leaving the club next summer.
The Brazilian, who was an unused substitute in Barcelona’s season-opening 4-0 win over Villarreal on Sunday, will be free to sign a pre-contract with any interested club in January.
Garcia, meanwhile, has made two appearances for Guardiola’s side this season as he continues to be strongly linked with a return to the club where he rose through the ranks of La Masia.