Lecavalier quickly became one of the league's more coveted free agents after the Tampa Bay Lightning bought out his contract on Thursday.
Bergevin says the possibility of signing Lecavalier depends on a variety of factors and it's too soon to say what he'll do.
"It will depend on many different things," Bergevin told reporters Saturday. "Contracts have been bought out and there will be others. Many things can happen before the opening of the free agent market on July 5."
Bergevin also wouldn't say whether he's working to sign Norris winner P.K. Subban to an extension before heading into the final season of a two-year contract. He said any negotiations would be confidential.
For the moment, the GM says his focus is on the draft.
The Canadiens may try to move up from the 25th spot in the first round, Bergevin said, and even that decision could be made only once the draft gets underway.
Trevor Timmins, the team's director of player development, said the team will be watching eagerly as their first pick approaches.
"Our wish list is ready and we hope that Santa Claus will give us what we want," he said.
The Habs hold six picks among the first 86 selections. There's a good chance they use one to get a goaltender, Bergevin said.
Bergevin also revealed that forward Colby Armstrong won't be back for another year. Armstrong had two goals and three assists in 37 games in his only season with the Habs.
The Canadian have three choices in the second round, including picks No. 34 and 36, which Timmins said were almost as good as first-round picks.
The extra draft picks were obtained in the 2012 trades that sent Andrei Kostitsyn to the Nashville Predators and Michael Cammalleri to the Calgary Flames.
The Canadiens also have two picks in the third round. A pick was acquired as part of the deal that sent Erik Cole to the Dallas Stars.
The Canadiens also have selections in the fourth, sixth and seventh round.