Mario Balotelli will miss the fixture with an ankle injury sustained before City's 1-0 loss to Sunderland, while Gareth Barry's red card against Liverpool on Tuesday rules him out through suspension.
Mancini will, therefore, seek to keep Yaya and Kolo Toure for an additional game before they leave for the Africa Cup of Nations.
"We tried to ask the Ivory Coast manager, because they have a meeting in Paris on Saturday, if Kolo and Yaya Toure can stay until Sunday," Mancini told reporters. "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 today or tomorrow."
The Italian was still contemplating his options for the match on Sunday, and revealed he might not have enough first team players available to name seven substitutes.
"For Sunday I think we have 17 players," he said. "I don't know how it is going to work. Gareth Barry is suspended, we don’t know about Yaya and Kolo, and Mario Balotelli is injured. He hurt his ankle before the Sunderland match."
Mancini added that Carlos Tevez could compete a transfer away from the club as soon as this week.
"I don’t know the situation today with Carlos," he said. "I hope for him that he can close a deal with one team this week."
Owen Hargreaves, meanwhile, has returned to full training and could be ready to play in the near future.
"Owen has worked with the team for the last week without problems," Mancini said. "Owen needs to play and to work."