Initial reports suggested he had torn a meniscus in his right knee with a recovery time of four months.
But at his press conference ahead of Saturday's trip to West Ham, Mancini revealed the right-back could even return before the end of November.
He said: "I think maybe - it is my opinion - three or four weeks. I read three months but I don't know why. One month - maximum.
"It is not bad. Maybe in three or four weeks he can start to play. He put only two stitches in his knee. For this reason, maybe four weeks."