According to Reuters, the Belgium international is recovering ahead of schedule after suffering the injury in training in August.
He has played just 31 minutes for City this season but said he is aiming to return in time for the Manchester derby: "I still need three, four, five weeks, but I'm getting there. Hopefully I can be back soon, help the team and perform well. I'm hoping to be back after the next international break. I think I will be back for the derby."
De Bruyne, 27, is arguably City's most important player.
In their record-breaking Premier League-winning campaign last term, he netted eight goals and provided 16 assists. Many people felt he should have won the PFA Player of the Year award ahead of Liverpool's Mohamed Salah:
City have been impressive in De Bruyne's absence this season, picking up 13 points from a possible 15 in the Premier League to sit third in the table.
However, they fell to a 2-1 home defeat to Lyon in the UEFA Champions League on Wednesday to end a 12-match unbeaten run in all competitions.
Pep Guardiola will want to have as many of his squad as possible fit as the busy winter period sets in, so it looks as though De Bruyne could be set to return at the ideal time.
If he is back in action in November, he should be back to match fitness by December, when the fixtures will come thick and fast and his influence could prove telling.