The club's top two veterans on the blue-line can become unrestricted free agents on July 1 and speculation has been rife that Souray will move on.
"The priority is to give Montreal a real good chance of signing me," Souray said Monday as the team met at the Bell Centre two days after they were eliminated from the NHL playoffs.
"We have lots of time. There's three months before anything has to be done. Montreal has been really good and I hope our relationship continues. I love Montreal. It's a challenge, but I enjoy playing here. But it's a business and we'll see what happens."
Souray set an NHL record for defencemen with 19 power-play goals, helping the Canadiens post the league's best success rate with the man advantage.
Despite his defensive woes - he was minus-28 - he is expected to draw big money offers on the open market.
The other point is manned by 28-year-old Markov, the team's best two-way defenceman.
"It's not all about the money," Markov said. "I like Montreal.
"It's a great team, great fans. I want to play on this team."
Gainey is expected to give an indication of where the Canadiens are headed when he meets with the media on Tuesday. Montreal missed the playoffs for the fifth time in eight seasons.
Checking forwards Radek Bonk and Mike Johnson, who earned US$2.4 million and $1.9 million respectively this season, can also become unrestricted free agents.
Two others, defenceman Janne Niinimaa and goalie David Aebischer, are expected to be set free to find other teams.
Gainey will also have to sign forwards Michael Ryder, Chris Higgins, Tomas Plekanec, Alexander Perezhogin and defencemen Mike Komisarek and Josh Gorges - all restricted free agents.
Souray injured his left shoulder in the third period of the final game of the season, a 6-5 loss in Toronto on Saturday night that pushed Montreal out of the playoffs. He is to have an MRI exam Tuesday to see what damage was done.
The main questions of the off-season may involve veterans Sergei Samsonov and Alex Kovalev.
Samsonov was a healthy scratch for the last 13 games of the season, after he questioned whether he made the right move in signing as a free agent last summer.
With one season at $3.5 million left on his contract, he may be bought out.
Kovalev has two years at $4.5 million per season left on his deal, and wants to return despite a dreadful season of only 18 goals and 29 assists.
He acknowledged he had a bad season, but when asked if he let the team down, Kovalev shot back: "I didn't let anybody down. I tried to do my best and if people think I didn't do my best, that's fine to me. Personally, I feel I did what I could."
Then, with a smile, he added: "You guys (reporters) will lose your job if I don't come back because you'll have nothing to write about."
Samsonov, who had only nine goals in 63 games this season, doesn't feel he's finished as an NHL player and doesn't know yet what he'll do if offered a buyout.
"If that happens, I'll decide then," he said. "Obviously that's not something I'm thinking of."
The Canadiens were one of the league's top teams in the first half of the season, but it all starting coming undone around late December.
They tried in vain to right a sinking ship by going 9-4 in the final four weeks, but wasted chances to clinch a playoff spot with losses to the New York Rangers and Toronto in their final two games.
"Some guys may have had individual motives instead of team (motives) and that may be why we went downhill," said Higgins. "We were going in different directions for a while and it spiralled out of control."
But he said there was a good atmosphere in the dressing room this season, despite some "individual incidents," such as the Samsonov and Kovalev situations.
Some questioned the leadership of captain Saku Koivu, who had a career years with 22 goals and 75 points, and whether he would ask out of Montreal.
Koivu said no, but . . .
"I want to be back, there's no question about that," he said. "But the reality is that we get older and how many years are in front of me, I don't know.
"I don't want to be part of a team that's going to rebuild and rebuild and not make the playoffs again. Hopefully, we can compete against the best and have a chance to win."
Koivu will have a cataract removed from his left eye this summer and will miss the world championships in Moscow.
Markov will definitely go to the worlds, while Kovalev, the Russian Olympic team captain, said he will go if he is asked.
Higgins and Komisarek are considering offers to play for the United States, and Aebischer and defenceman Mark Streit will play for Switzerland.
If goalie Cristobal Huet wanted to play for France, he'd have to go to Japan to play in the B pool. He won't.
"My heart's there, but my body isn't," Huet said.