Traverse, who played for Montreal from 2000 to 2003, was signed by San Jose from the Dallas Stars this summer. He played in two pre-season games for the Sharks.
Head coach Guy Carbonneau said he was waiting for results of tests on Souray's shoulder injury, which forced him to be scratched from a game Tuesday night against Tampa Bay.
"Hopefully, it will be good news," Carbonneau said.
The Canadiens were already missing veteran rearguard Francis Bouillon until November with a knee injury, while their top reserve defenceman Jean-Philippe Cote is also injured.
Traverse, 32, spent most of last season with Iowa in the AHL. The Montreal native broke into the NHL in 1995 with Ottawa. He has also played for Anaheim and Boston.
It is uncertain how Traverse's arrival will effect the battle for defence jobs in camp between hopefuls Dan Jancevski, Ryan O'Byrne and Andre Benoit.
They were to get a last look in a pre-season game Thursday night in Ottawa.
Carbonneau said he wants to make his final cuts as soon as possible and have the 20 players who will dress for the season opener on the ice for the final exhibition game Saturday night against the Senators in Montreal.
The cuts could come as early as Friday, when the debate on whether to keep 19-year-old Guillaume Latendresse is to be settled. The Montreal-area native is battling Andrei Kostitsyn for a job at forward.
For a second year in a row, there has been passionate public support for Latendresse, a physical winger who has been one of the most eye-catching young players in camp.
Kostitsyn, a quick, skilled right winger, has also played well and has two years of minor-league experience to draw on.
If he is cut, Latendresse would be returned to the junior Drummondville Voltigeurs. Kostitsyn, a first-round pick in 2003, can be returned to AHL Hamilton without clearing waivers.
A poll published in Le Journal de Montreal on Wednesday showed 75 per cent of Quebec hockey fans wanted the Canadiens to keep Latendresse.
"It's fun to see, but it's like the coach said, it's not the people that are going to put me on the team, it's me and how I play that's important," said Latendresse.
Last season, he struggled after returning to Drummondville after a standout camp in Montreal. If it happens again "it'll be tough, but it's not my decision, so I'll have to work with it," he said.
Carbonneau said there was no question of keeping Latendresse only for a few games.
"If he's on the team, he'll be here for the year - not one game or five games or 10 games," said Carbonneau. "We'll work with him to make him a good player.
"No one wants him to start here thinking that every game is crucial and that if he has one bad game he'll be sent back. If he's here, he's here (to stay)."