Bergevin added Julien's health situation is not related to COVID-19 but it's unlikely he'll return to the bench during the team's first-round playoff series against the Philadelphia Flyers, per TSN's Frank Seravalli.
The Flyers scored a 2-1 victory over the Canadiens in Game 1 on Wednesday night.
Julien is in the fourth season of his second stint as Montreal's head coach. He previously served in the same capacity from 2002 through 2006, which was his first head coaching job.
The Habs entered the restructured 24-team playoffs, a change caused by the coronavirus pandemic, as the No. 12 seed in the Eastern Conference. They upset the Pittsburgh Penguins in the qualifying round despite a lackluster 31-40-9 record during the regular season.
Julien was impressed with how his team responded to the challenge.
"It's not so much what you learn, but it's what we were able to prove," he said. "I always felt we had good leadership, good character. We're a young team. We had some areas there that, during the season, we wanted to see improve. And we've got an opportunity, here in the playoffs, to come and play under pressure situations, and what I've liked about our team is how well we handled it."
The 60-year-old Ontario native has compiled a 658-440-10-148 record across 18 years as an NHL head coach with the Canadiens, Boston Bruins and New Jersey Devils. He led the Bruins to a Stanley Cup championship in 2011.
Muller is a former NHL center who played for the Habs from 1991 through 1995. He posted an 80-80-27 record in three years as the Carolina Hurricanes' head coach from 2011 until 2014.
He joined Julien's Canadiens staff in June 2016.
Game 2 of the series between Montreal and Philadelphia is scheduled for Friday afternoon at 3 p.m. ET at Scotiabank Arena in Toronto, the host city for the Eastern Conference's bubble.