The Catholic Church has largely maintained a celibate priesthood for centuries. Although the practice could be changed by a pope, it would be a major shift in doctrine that pontiffs have resisted for decades.
Johan Bonny, bishop of Antwerp in Belgium since 2009 and known for taking progressive positions, said in a public letter to his parishioners that he would make "every effort" to ordain married men within two years and would identify men to train as priests.
Bishops in the 1.4-billion-member church vow obedience to the Pope and it is very unusual for them to announce they are considering an action that may contradict church teaching.
If Bonny went ahead and ordained married priests without the Vatican's permission, he could be subject to excommunication, a formal expulsion from the church.
A Vatican spokesperson did not immediately respond to a request for comment on Bonny's remarks.
Leo, who took leadership of the church last year after the death of Pope Francis, has not spoken at length about the possibility of married priests but has spoken positively about celibacy on several occasions.
Francis, who pursued a range of reforms during his 12 years as Pope, firmly ruled out the possibility of married priests.
In his letter, Bonny said ordaining married men would be a response to the decline in the number of men willing to maintain celibacy in order to become priests, saying the current replacement rate is "just above zero".
"The question is no longer whether the church can ordain married men as priests, but when it will do so, and who will do it," he said. "Any delay comes across as an excuse."
Bonny did not say whether he would go ahead and ordain married men if he did not receive papal permission.
The debate over whether Catholic priests should be allowed to marry has rumbled for centuries, but Francis reignited interest in the issue by holding several summits of bishops about possible reforms in the church.
A 2018 Vatican summit of bishops formally asked Francis to ordain married priests, which he did not do.
Last year the Vatican said the number of men studying for the priesthood had seen an uninterrupted decline since 2012.
Proponents of letting priests marry say it would attract more men to the priesthood. Opponents say celibacy allows a priest to dedicate himself entirely to the church.
