We understand City are optimistic that Kun could play some part in the FA Cup Third Round replay against Blackburn on January 15.
The idea would be to give Aguero a run out against Blackburn, possibly a cameo off the bench to ease him back to match fitness, ahead of the Premier League clash against Cardiff the following weekend.
Aguero has been out of action since the 6-3 win over Arsenal in mid-December, where he picked up a calf injury after earlier opening the scoring.
He has recovered well, but City are determined not to rush him back after seeing Kompany suffer a recurrence when hurried back earlier this season.
City have coped well without their leading goalscorer, winning all four league games, but his return during such a busy period will be a major boost.