It has been reported that priests who show "inappropriate sexual tendencies" are removed for "a period of training, personal reflection and enlightenment," according to The Independent.
The revelation has come to light as the Synod on the family gets under way in Rome.
Over the weekend a senior official, Monsignor Krzysztof Charamsa was sacked, hours after publically coming out as homosexual.
Former clergyman Mario Bonfante claims he was told to go to the Venturini monastery, in Trento, when his seniors discovered he was gay so that he can "rediscover the right path".
According to the Telegraph, he said: "It's a place where they help you to rediscover the straight and narrow.
"They wanted to 'cure' me but I refused to go."
After he refused he says he was dismissed.
Fr Gianluigi Pasto, 72, in charge of the monastery told an Italian newspaper: "I can only say that here we help the priests become healthy."
Fr Gianluigi Pasto has denied that the institution is there to deal with gay priests, or priests with paedophile tendencies.
He added: "Right now we have neither gay priests nor paedophile priests here.
"Certainty our job is to welcome everybody."
Gay rights groups have reacted angrily to these reports, Francis DeBernardo, Director of New Ways Ministry (a US LGBT Catholic rights group), told The Independent: "Being gay is not a disease that needs to be cured... What needs to be cured is not homosexuality but homophobia."
Speaking at the Synod, Pope Francis stressed that the Church should have the courage to evolve if that is what God wants.
The Vatican has declined to comment.
