The 63-year-old man thought to be Neville Neville was bailed until May pending further police enquiries.
Mr Neville's two sons Gary and Phil both played football for Manchester United and England while daughter Tracey played netball for England.
He is a former director of Bury Football Club, where wife Jill is still club secretary.
A man arrested on suspicion of indecent assault is believed to be Neville Neville, the father of former England footballers Gary and Phil, ITV News understands.
Police said they arrested a 63-year-old man after reports of an incident in Bury in the early hours of Saturday.