The 27-year-old has been in custody at HMP Altcourse in Merseyside since Friday, when he appeared at Chester Magistrates’ Court charged with four counts of rape and one sexual assault.
A bail application was denied during a 50-minute hearing held behind closed doors at Chester Crown Court on Wednesday.
Mendy, who also plays for the French national team, did not attend court.
Honorary Recorder of Chester Judge Steven Everett refused the application, a court spokesman said.
Mendy is charged with attacks on three different women, including one under 18, at his home on Withinlee Road in Prestbury, Cheshire.
Three of the rapes are alleged to have taken place in October 2020 and he is accused of sexually assaulting a woman in early January this year.
He is also charged with raping a woman last month.
The footballer, who has been suspended by the club pending investigation, is due to appear at Chester Crown Court on 10 September.
A second man, aged 40, was arrested on suspicion of rape as part of the police investigation into the allegations but was released on bail, Cheshire Constabulary said.
Additional reporting by Press Association