Adebayor is currently in Togo on compassionate leave following the machine-gun attack on the national team bus that saw three people killed as they arrived in Angola for the African Nations Cup.
City have told Adebayor to take whatever time he needs but Mancini says that the former Arsenal striker "will be back in the next few days".
Mancini also expects Patrick Vieira to be ready for the second leg, with an FA Cup debut at Scunthorpe on Sunday a possibility as the French midfielder recovers from his calf injury.
Stephen Ireland has recovered from a hamstring injury and is also in Mancini's thoughts for the return match against United.
City hold a 2-1 advantage going to Old Trafford, thanks to a brace from former United striker Carlos Tevez after Ryan Giggs had opened the scoring.