The influential defender was ruled out for at least a month after limping out of City's season-opening Premier League win against Newcastle on August 19.
Kompany has said he hopes to return inside a month - possibly for the trip to Stoke on September 14, or the start of the Champions League campaign three days later - but manager Manuel Pellegrini has warned he will not be rushed. Pellegrini said: "(There is) nothing new with Vincent.
"Doctors said from the beginning it could last for six weeks. We will see next week how he improves but less than one month is impossible."
City have been heavily linked with Atletico Madrid's Martin Demichelis, who worked with Pellegrini at Malaga, and a deal could move closer if the Spanish side secure Ajax's Toby Alderweireld as a replacement.
There have also been reports linking City with Porto's £38million-rated Eliaquim Mangala, but that would seem unlikely given the apparent interest in Demichelis, as well as the cost.
Pellegrini said: "There are a lot of names linked with Manchester City. It is not my duty to answer (on) all those names.
"We will see next Monday what will happen.
"We have some days to bring someone in. We will see what we can do."