The 25-year-old damaged his cartilage and lateral meniscus in a challenge with Brighton & Hove Albion's Adam Webster and had surgery in September but is now back training on grass on his own.
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Third-placed City, who failed to replace Vincent Kompany in the close season, have struggled during Laporte's absence with fellow central defender John Stones also battling injuries, and the side are 14 points behind leaders Liverpool.
"He (Laporte) is getting better. He is training alone but already on the pitch," Guardiola told a news conference ahead of Wednesday's league clash against 10th-placed Everton.
"He is in the last part (of his recovery). In one week or 10 days he can start to train with us... The rest (of the team) are OK."
Stones has not featured since City's derby defeat at home by Manchester United earlier this month due to a thigh problem, but is back training along with midfielder David Silva who has shaken off a knock.
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Guardiola said he expected a tough test against Everton, who are unbeaten in five games, including back-to-back victories in their last two matches under new manager Carlo Ancelotti.
"Everton are one of the biggest traditional clubs in England with incredibly strong players. They have struggled for points but the quality is there," Guardiola added.
"They have a new manager who has incredible experience. He is one of the smartest guys, he is always able to make them work to get good results.
"It will be a difficult test for us.. I know Carlo well... I think it is incredible for English football that he is back and I am pretty sure he will be a success."
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