The Spain international started in Wednesday’s Champions League victory over Porto with his contract set to expire at the end of the season
The 19-year-old is in the final year of his contract and has made it clear that he wants to leave the club and join Barcelona, who tried to sign him during the last transfer window.
Barca made Garcia their priority transfer target but the two clubs could not reach a deal on the final day of the transfer window.
The Spanish giants will make a renewed bid for the defender when the transfer window reopens in January, but Guardiola has not given up all hope that he will remain at the Etihad Stadium.
“I know he wanted to leave but he’s going to stay and maybe we can seduce him in this year to extend the contract with us,” Guardiola said after the 3-1 victory.
“He’s a guy who is so stable in many many things and we are so happy.”
With Nathan Ake and Aymeric Laporte injured, Garcia was still something of a surprise starter against the Portuguese champions.
John Stones was left on the bench and only came on for the final few minutes when Fernandinho hobbled off with a knee injury.
Ake was left out after suffering what Guardiola described as “niggles in the groin” on the morning of the match. The City boss decided to leave him out of the squad to rest and recover full fitness.
Laporte, meanwhile, is expected to return to training on Thursday but will face a race to be fit for Saturday’s trip to West Ham.
Ruben Dias started his third consecutive game since his £62m ($79m) transfer from Porto’s big rivals Benfica.
The Portuguese international was at fault for the opening goal when he gave the ball away with a sloppy pass which was punished by Luis Diaz. However, Guardiola was happy with his defence despite conceding the game’s first goal for the first time this season.
“They have the winning mentality, they have to win every game.
“I was surprised they played so defensively with five at the back, we had to be patient but in the second half we didn’t concede counter-attacks, we didn’t concede set-pieces, we didn’t allow them to run.
“We did the perfect performance against a really good team. It is nice to win games while suffering.”