The centre-back has been out of action since New Year’s Day after injuring his hamstring in the draw at Norwich City.
Sakho has been forced to watch his Palace team-mates from the sidelines and had been working indoors to get fit.
However, the Frenchman is now out on the grass and taking part in training matches.
Palace have missed Sakho, with Saturday’s win over Newcastle their first in his absence.
The Eagles face a trip to rivals Brighton this weekend, but that match may come too soon for Sakho given he is likely to be short of fitness.
The 30-year-old has battled with injuries all season, restricting him to just eight Premier League appearances.
The defender will now hope that his fitness troubles are behind him as he looks to help Palace kick on towards the end of the season.