The six-time Ballon d'Or winner has told Barcelona he wants to leave and did not show up for the first day of pre-season training under Ronald Koeman on Monday.
He remains in dispute with the Catalan giants over the possible terms of his departure, with Goal reporting that he considers his current contract, which is due to expire in 2021, to already be finished.
City are one of a handful of clubs reported to be in contention to sign Messi, with a reunion with former Barca boss Pep Guardiola an obvious attraction.
Though the saga has sent shockwaves through world football, Garcia insists the City squad have not been discussing the possibility of playing alongside the Argentine.
Speaking to reporters at a news conference with the Spain squad, the 19-year-old said: "At City we have not talked about Messi coming, but everyone would like to have Messi in their team.
"On the Messi issue, it's something between clubs that I can't get into.
"I am going to avoid the question if he would be a good signing for City because he is a Barca player and not I'm going to comment on it. "
While Messi continues to be linked with a move to the Etihad Stadium, Garcia has been touted for a move in the opposite direction.
The defender is into the final 12 months of his contract with City, having rejected the offer of a new deal.
Barca have reportedly made Garcia one of their top transfer targets and are ready to submit an offer in the region of €15 million (£14m/$18m) to bring the player back to the club.
When pressed on his future Garcia played down talk of an imminent departure, suggesting he could see out the final year of his City contract and leave on a free transfer next year.
“I told City that I will not renew my contract, but still I have one season with them and hope to return,” he said.
“My goal is to train and play as much as possible to show here [with the Spanish national team] and in Manchester that the coach can count on me.
"What comes next is something I don't know. I can’t control. I focus on what I can control."