He said the vast majority of Uber's drivers work part-time and there are no training requirements in any other Canadian city.
Forcing all Uber drivers to undergo a mandatory 35 hours of training, as Transport Minister Laurent Lessard announced last week, will make it impossible for the company to continue its operations in Quebec beyond October 14, Guillemette added.
Ride-hailing company Uber says it will cease operating in Quebec next month if the province doesn't rescind new rules introduced last week.
Quebec's transport ministry did not immediately respond to a request for comment.
Additionally, Lessard said all Uber drivers will be required to undergo the same number of training hours as do drivers of traditional taxis, which is 35 hours.
"I am very surprised that a big company, a big multinational like Uber, can't find a way to use its application to train its drivers", the transport minister said at a news conference in Quebec City.
Under the new rules, Uber driver background checks must be conducted by the police and no longer by private companies.
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"I am firm in my intention", Lessard said.
The company left room to reverse its decision, calling on the government to reconsider regulations announced on Friday that tightened up the rules of a pilot project that had let Uber operate since October past year.
"We can negotiate with them, but not on the basis of those two things", Gaudreault said.
The La Presse report, citing unnamed sources, says the announcement of Uber's departure could come as early as Tuesday, and had been decided by the service's head office in San Francisco last weekend.
The regulations come a year after the provincial government agreed to let Uber operate on a trial basis. Due to lower overhead, they were able to undercut the traditional taxi industry and cabbies argue the value of their permits have diminished significantly as a result.
Under the terms of the original pilot project, Uber drivers were only forced to take 20 hours of training.
Guillemette said the number of hours worked by an estimated 10,000 Uber drivers in Quebec past year were equivalent to 3,000 full-time jobs in the province.