Katumbi is awaiting trial for the alleged recruitment of mercenaries and has already been sentenced to three years in jail.
In a confidential report seen by AFP on Wednesday, the Congolese Episcopal Conference (CENCO) demanded that the government reverse its orders for Katumbi -- who has set his eyes on the presidency -- to be immediately arrested if he returns from abroad.
Katumbi, a powerful businessman and ex-governor of the mineral-rich Katanga province, should be allowed to "return as a free man and exercise his civil and political rights," the Church said in the report, which was sent to President Joseph Kabila on March 29.
The bishops issued the report as part of a New Year's Eve deal brokered by the Church to end the crisis sparked by Kabila's refusal to step down after his mandate ran out on December 20.
Signatories to the deal -- excluding delegates from the ruling majority -- charged the bishops with gathering information that could allow Katumbi and fellow opposition politician Jean-Claude Muyambo to operate freely in DR Congo.
Katumbi, a former Kabila ally who switched to the opposition in September, is awaiting trial for the alleged recruitment of mercenaries and has already been sentenced to three years in jail for seizing a building belonging to a Greek citizen.
Muyambo was sentenced to five years on fraud charges linked to the same building.
"The two trials are simply a farce," the bishops' report said, adding their investigation had found Katumbi was charged on the basis of fabricated evidence "with the sole goal of bringing him to trial and convicting him".
This suggests that Katumbi's trial was "a purely political settling of scores", the report added.
Government spokesman Lambert Mende told AFP the Church should address its requests to the courts rather than the president.
"Freedom is not obtained in this manner," said Celestin Tunda Ya Kasende, a spokesman for the ruling majority, adding the Church should not put forward any proposals offering "privileged treatment for tie-wearing criminals".
Katumbi, the charismatic owner of a football club, was named as a presidential candidate by the G7 group of opposition parties for the election that was due to take place at the end of 2016.
Under the power-sharing deal reached on New Year's Eve, DR Congo is now set to hold an election by the end of 2017.