The Italian-born manager and former player has been at the club for over 30 years
Crewe director of football Dario Gradi has been suspended by the FA after claims he "smoothed over" a player's sex abuse complaint.
The former Crewe manager released a statement last month insisting he was unaware of the alleged sex abuse that took place at the club.
His response follows revelations by former player Andy Woodward that he was abused by Barry Bennell while at Crewe when he was aged between 11 and 15-years-old.
Gradi, who has worked as a manager and academy manager during his 33 years at Crewe, said in a statement last month: "I would like to express sympathy to the victims of Barry Bennell, not only at Crewe Alexandra, but at other clubs in the North West.
"The first I knew of Barry Bennell's crimes was when he was arrested in the United States in 1994. I knew nothing of his crimes before this time when he was employed by us."
Bennell was jailed for nine years in 1998 after pleading guilty to committing sex offences.