Kompany sustained a calf strain in the FA Cup fourth round defeat of Stoke City late last month, and had to watch the majority of the encounter from the sidelines as Pablo Zabaleta's goal ensured City progressed.
The 26-year-old Belgium international was initially feared to be missing for around a month but, it is claimed, Kompany could even make a return in time for the weekend meeting with Southampton.
Kompany's fitness will be vital to Manchester City in the final months of the season, as Roberto Mancini's side look to make up a deficit of nine points on Premier League leaders Manchester United.
City have failed to win either of the matches that Kompany has missed so far, with a goalless draw with bottom club Queens Park Rangers followed by a 2-2 scoreline against Liverpool last weekend.
Liverpool had 21 shots on the Manchester City goal in the meeting at the Etihad Stadium, 12 of which were on target.