The 19-year-old has broken into the first-team fold under Pep Guardiola and started in City’s 4-0 win over Liverpool.
However, his contract expires in June 2021 and Barcelona are known to want him back.
Barca’s plan was to convince centre-back Garcia to join them when his deal ends, but things have taken a turn.
According to SPORT, the Catalans are eager to get their former La Masia talent back as soon as possible.
The publication adds that if City and Barcelona can reach an agreement, it is likely to be later this summer.
Talks are at a very early stage and City would prefer to wait until the season is over to deal with transfers.
Much will depend on if Garcia accepts a new contract offer from the Premier League club.
If he doesn’t, then the door will be wide open for him to return to Barca, who have monitored his progress since he left in 2017.
Garcia has appeared eight times in the league for City this season, playing a total of 448 minutes.
He has made further appearances in the Champions League, FA Cup and Carabao Cup, bringing his total number of appearances to 13.