The club have released images of the 29-year-old back on the training field accompanied with a positive update on his fitness on the official website.
The influential Belgium defender has been hampered by all-too-familiar calf problems this season and has not featured since an abortive comeback attempt against Sunderland on Boxing Day.
Kompany managed just nine minutes in that 4-1 Barclays Premier League victory at the Etihad Stadium - his only action in City's last 19 matches.
There has been doubt over when Kompany might return but manager Manuel Pellegrini expressed hope last week that Kompany could be back within a fortnight.
Kompany's current lay-off is his 12th with a calf injury since the start of the title-winning 2011-12 campaign and the player has seen specialists in an attempt to get to the root of the recurring issue.
Pellegrini is likely to give an update as he holds a press conference to preview Saturday's top-of-the table clash against Leicester on Friday.
Source: PA