The Spaniard was part of Barcelona's La Masia, but departed in 2017 to join Man City, where he has risen to the first team.
Garcia initially struggled for minutes under compatriot Pep Guardiola, but impressed in the latter stages of the 2019/20 campaign, starting five of the Sky Blues' final seven league matches.
Guardiola is said to be a big fan of the 19-year-old and has previously openly praised Garcia for his footballing intelligence and ability to read the game. However, now in the final year of his contract, Guardiola admitted in August that Garcia does not want to sign a new deal with the club as he is keen on a move elsewhere - specifically a return to Barcelona.
It has been suggested Barça may wait until next summer in order to sign him on a free transfer, but Alfredo Martinez has told El Transistor that La Blaugrana have already made a €10m (£7.2m) offer to sign him. There is no mention of whether this has been accepted or rejected, but it will likely be the latter as City have previously demanded a lot more than the offer made.
SPORT also report that the Catalan giants have made an offer for the defender, but rather than €10m in one sum, they claim the offer is €8m with €2m in add-ons.
The report further adds that while the Sky Blues were previously holding out for as much as €40m in order to part ways with Garcia this summer, they could now slash their asking price in half.
City have attempted to persuade Garcia - who recently made his senior debut for Spain - to stay at the Etihad, but this has proven unsuccessful so far as he has his heart set on a return home.