The player, who has not been named for legal reasons, was arrested on Friday and has been released on police bail.
CNN has not named the club to avoid identifying the player.
The club announced the player’s suspension on Monday, pending the police investigation.
Greater Manchester Police (GMP) said in a statement to CNN Tuesday: “GMP officers arrested a 31-year-old man from the Bowdon area of Trafford on Friday 16 July 2021, on suspicion of child sex offences. He is on police bail pending further enquiries.”
The soccer club is preparing for the new Premier League season, which begins next month.