The La Liga club have included a buyout clause of 400m euros (£343m) in the 20-year-old’s contract.
Garcia’s youth career began at Barcelona before he moved to Manchester City in 2017.
On Monday, Barcelona agreed a two-year deal with City striker Sergio Aguero, whose contract expires on 30 June.
Garcia, who joined Barcelona’s academy in 2008, made 12 appearances for Pep Guardiola’s Premier League champions in 2020-21 but started just three games in their title-winning campaign.
The Spaniard made 35 senior appearances in all for City, with 20 of those coming in the 2019-20 season when he was a regular starter for Guardiola as his squad was depleted by injuries.
He has featured seven times for Spain since his debut last September and has been included in Luis Enrique’s Euro 2020 squad.
Ronald Koeman’s Barcelona finished third in La Liga, seven points behind champions Atletico Madrid.
Source: bbc sports