The goalkeeper ruptured his Achilles tendon during a practice game in training after just two Premier League games.
He is now nearing a comeback ahead of the end of the season and the Copa America.
"[He took part in] the first part of the training session on the pitch, it was a long, long injury," said manager Pep Guardiola.
"After the surgery, he had a little bit of infection, take more time to recover. He is optimistic and it is to recover well."