Laporte damaged cartilage and the lateral meniscus in his right knee after a challenge on Brighton & Hove Albion's Adam Webster and had surgery in September but is now back training on grass on his own.
"He is training every day and has finished the training with a good feeling and no pain," Guardiola told a news conference ahead of City's trip to Aston Villa on Sunday. "I don't know honestly when he will be ready to play some minutes but of course it is closer. He is moving really well so I think the operation was good."
In Laporte's absence, defending champions City have struggled defensively and slipped 14 points behind league leaders Liverpool, having played a game more than Juergen Klopp's side.
"Aymeric with his left foot, plays the left side and he is quick," Guardiola added. "He settled quickly in this league since he arrived. Of course (his return) is important for us but we have to respect the process."
Another City player recovering from a long-term knee injury is winger Leroy Sane. German media have recently reported that Bayern Munich's long-standing interest in him has been put on hold until the end of the season.
When asked about Sane's future at the Etihad Stadium, Guardiola said: "It is a question for Leroy, his agents and the club. I am not involved in that. I know him well. I was the guy who pushed for him to come here even though he didn't play regularly for Schalke. I want him to come back fit now, his knee looks really good, after that it's not my business. His own future is not in my hands."
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ