The government is expected to make the announcement Sunday, according to Radio-Canada sources.
Drivers will need to obtain a copy of their records from police, or possibly from the taxi bureau, at their own expense.
According to Radio-Canada, a new provincial committee will be responsible for reviewing the records.
That committee will consider the number of offences and severity of the crimes, the context in which they were committed and the steps taken since, including requests for pardons.
If they’re cleared to drive a taxi, a permit will be issued by the taxi bureau in Montreal and at the SAAQ outside the city.
The move comes as pressure mounts to crack down in the wake of a string of reports of sexual assaults by drivers.
In July, CBC Montreal reported the story of one woman who said she was assaulted by a cab driver after hailing a taxi on the street.
A month later, Montreal police issued an appeal for information after four women reported they had been sexually assaulted by a taxi driver Notre-Dame-de-Grâce.
Police said Friday that investigation is still ongoing and no arrests have been made.
In October, police said they investigated 17 cases of sexual assaults in taxis in 2014, a small number, they said, given the number of taxis in service in the Montreal area.
Mandatory in other cities
In most major cities across Canada, taxi drivers are required to pass a criminal background check, but in Montreal and across Quebec, there are no safeguards in effect to stop passengers from hopping into a cab with a convicted felon.
Quebec law states that taxi permits will not be issued to anyone who’s been "convicted, in the last five years, of an indictable or criminal offence connected with the aptitudes and conduct required to carry on the occupation of taxi driver.”
However, the law hasn’t been enforced because of a squabble over whose responsibility it is to check.
Last fall, Quebec's Ministry of Transport said it was planning to require those applying for a taxi driver's permit to submit a $70 criminal background check by Montreal police.
At the time, the ministry said it was still in the process of deciding which crimes would warrant a taxi driver's license being rejected.
In September, Quebec transportation ministry said enforcing criminal background checks for taxi drivers is at the top of its priority list, but would not say when new measures would be in place.
Currently, the only taxi drivers who must submit to a criminal background check are those working with vulnerable populations including children and the elderly.