He was detained at United's training ground at Thorp Arch and held overnight at Chapeltown police station for further questioning today.
A second man, not associated with the team, was also being questioned by police.
The woman claims to have been assaulted in the Leeds area on Monday night.
Today a police spokeswoman said: "All I can confirm is that two men are still in custody."
Detectives were granted permission this afternoon to hold one of the men, believed to be the man named in the paper, for a further 12 hours.