City manager Hébert resigned Monday at Mayor Michael Applebaum's request, amid allegations he lied about trying to have the city's police chief fired.
Bergeron told CBC's Daybreak that he finds it difficult to trust many people in Montreal politics.
"It's unbelievable that a man in this position can lie to the mayor of Montreal. It's incroyable!" he said.
"He lied to the mayor, he lied to the city council, he lied to Montrealers."
As for Hébert's interim replacement, Jean-Yves Hinse, Bergeron says he has his doubts about him.
"Frankly, I don't trust him more than anybody else," he said.
The only person the Projet Montréal leader says he would trust as the city's manager is Rachel Laperrière, who currently serves as deputy minister of culture and communications for Quebec.Laperrière worked for the city from 2001 to 2012, at one time serving as acting general manager.
"We need Rachel Laperrière … it's time for her to be the director-general of the City of Montreal," Bergeron said.