The pair are due to report for African Nations Cup duty with the Ivory Coast, but manager Roberto Mancini has requested that they be allowed to miss a team meeting in Paris on Saturday, and the first part of a two-week training camp in Abu Dhabi that begins on Sunday.
"We have asked the Ivory Coast manager because they have a meeting in Paris on Saturday," said Mancini.
"We have asked whether Kolo and Yaya can stay with us and then they can go to Abu Dhabi. We are waiting for an answer and I expect to know either [Thursday] or [Friday]."
Mancini is nervously awaiting an answer because the City manager has warned he may not have enough players to fill his substitutes bench at the weekend.
Gareth Barry is suspended, Owen Hargreaves is not considered fit enough to be involved and Mario Balotelli is troubled by an ankle injury that prevented him playing against both Sunderland and Liverpool.
Mancini said: "We have 17 players. I do not know how it is going to work."
City officials have distanced themselves from reports that both QPR and Wolves have lodged bid for Nedum Onuoha.
However, it does appear Carlos Tevez will be moving on amid reports he has opened negotiations with Inter Milan.
"I do not know the situation but I do hope for him he can close a deal with a team this week because he hasn't played for three months."