Police issued a picture of a suspect after reports a man with a three-month-old baby was asking people to buy the child in Barton Arcade on Sunday.
A 28-year-old man, arrested on suspicion of child neglect, has been bailed until September.
The baby's mother was reported missing last month, police said.
The baby girl is safe and well, added a police spokesman.
The mother of a baby, who it's claimed was offered for sale in Manchester city centre, was reported missing three weeks ago, police have said.