Mbappe was substituted after pulling his hamstring in a 4-0 Ligue 1 defeat of Toulouse last month.
The France forward has been working hard on his recovery over the international break but is not yet ready to return to training.
Edinson Cavani, though, is closer to making his comeback after he was injured in the same game as Mbappe.
In an update posted to PSG's official website on Thursday, the club said the Uruguay striker will make a "progressive return to training this week".
Thilo Kehrer and Julian Draxler are undergoing treatment with both players expected to miss the Week 5 home game against Strasbourg as a result.
Mbappe and Cavani are unlikely to be fit to take on Real Madrid, however, with PSG opening its UEFA Champions League campaign at home to the Spanish giant on Thursday.
Neymar is also ruled out of that game due to suspension, so PSG manager Thomas Tuchel could be without all three members of his usual front line for the Group A clash.
Former Stoke City forward Eric Maxim Choupo-Moting, who has scored three goals in two Ligue 1 games, is therefore in line to feature.