The veteran Ivorian is currently without a club after seeing out his contract at Galatasaray, and has been heavily linked with a one-year Stamford Bridge comeback.
But rumours in the past few days have suggested that City were considering a rival move for the 36-year-old following news that Alvaro Negredo will miss several months of action trough injury.
However, it is understood that Manuel Pellegrini has no interest in the powerful African striker, leaving the path clear for Chelsea.
Jose Mourinho is said to be keen to bring Drogba back as short-term cover for Diego Costa and Fernando Torres for the coming campaign with a view to him becoming a coach in west London.
The pair have a great working relationship following their successful first spell together at the club, and the experienced ace is likely to spurn big offers from Middle Eastern outfits for a sensational return.
Drogba is widely seen as one of the best strikers to have ever played for Chelsea, with his last act for the club having been a Champions League winning penalty against Bayern Munich in 2012.
From there he joined Chinese Super League side Shanghai Shenhua before leaving to play in Turkey with Gala.