The former Barca youth player wants to return to Spain, and the club are hoping to sign him this summer.
But ESPN reports the Catalan giants will not go over €15 million, considering Garcia is out of contract in a year.
They could sign the player on a free next summer, and would prefer to do a reasonable deal this summer.
But if City demand a mega fee, Barca will walk away knowing the player wants to come there eventually.
City want roughly €30 million for Garcia, who has become a first team member under Pep Guardiola this season.