Laporte, who joined from Athletic Bilbao in January 2018, is unsure exactly when he will be back but provided a positive update for City fans.
"[My recovery] is going very well," he told The National.
"I still need time but I hope as soon as possible I can come back and play with my team-mates. I can't say when exactly but more or less one-month-and-a-half to two months."
City's decision not to sign a centre-back to replace club legend Vincent Kompany came under further scrutiny following Laporte's injury.
In his absence, Pep Guardiola's defending champions have fallen 11 points adrift of unbeaten leaders Liverpool in the Premier League.
But Laporte insists City can once again pip Liverpool to the title having beaten the Reds by a solitary point in a thrilling race last term.
"Yes, of course [City can win the title]," Laporte added.
"Last year was quite similar when they had a similar lead but we still have time this year to recover, to catch them and to again try to win the Premier League, so we hope we can do that.
"We need to make sure we work a lot and don't lose any more games."