Kovalev, who has missed seven games with a sore elbow, skated in drills and took shots in practice on Sunday and pronounced himself 70 per cent certain to return for Monday's game (7:30 p.m. ET).
Rivet, who sat out nine games with pneumonia, says he's ready even if his conditioning is not completely back to normal.
"It will take time to be 100 per cent, but I've worked hard all week with the trainers to try to open up my lungs a bit and get into the best shape possible," Rivet said. "I feel pretty good on the ice now."
While Montreal should get players back, the rival Leafs are still missing regulars Darcy Tucker (foot), Kyle Wellwood (sports hernia), Michael Peca (broken leg), Pavel Kubina (broken finger) and Boyd Devereaux (sore wrist).
But injuries haven't stopped Toronto from vaulting back into the playoff picture by taking at least one point in 13 of their last 16 games (10-3-3).
The 30-23-9 Leafs are 10th in the NHL Eastern Conference, one point behind 32-26-6 Montreal, which is just out of playoff position in ninth place.
Montreal is 2-2-1 against the Leafs this season, with both wins by shoot-out.
Toronto is coming off a 5-2 win at last-place Philadelphia while Montreal ended a three-game winning run with a 3-2 defeat Saturday against the eighth-place Islanders in New York.
"There are teams you need the two points from - Philadelphia - and there are teams you're fighting with, and those are different points," Toronto coach Paul Maurice said. "Both teams know the value. It should be a great game."
Kubina and Devereaux skated Sunday at the Bell Centre, but aren't ready to return. Veterans Mats Sundin, Bryan McCabe, Tomas Kaberle, Hal Gill, Alexei Ponikarovsky and Nik Antropov opted to sit out the practice.
The Leafs have leaned on Andrew Raycroft, who will make his 24th consecutive start in goal, captain Sundin and strong play by the supporting cast, especially some youngsters, to get through their injuries.
"They've kept us in the fight," said Maurice. "We had to make it to the all-star break to have a chance to survive and since then, we've been a very good team.
"We've been able to survive because of Greg Gilbert and the job he's done with the (AHL's Toronto) Marlies. Having them in town, right there, and having an NHL coach with them has made a big difference."
And he was pleased to get forward Andy Wozniewski, who was injured in the third game of the season against Montreal, back for the game in Philadelphia.
"He played exceptionally well and skated well," said Maurice.
He had not yet decided whether recent call-up Jeremy Williams would dress after sitting out on Saturday.
The Canadiens had centre Steve Begin back on the ice Sunday, although he skated in a sweatsuit.
Begin broke his right foot while blocking a shot against Columbus on Feb. 18 and may be ready to return either Tuesday against the Rangers in New York or later in the week. He will wear a guard on his skate in case he is hit there again.
Montreal remains without goaltender Crostobal Huet, who is out for the rest of the regular season with a torn hamstring.
His replacement, 21-year-old Jaroslav Halak, won his first three NHL starts before dropping a game to the Islanders. Coach Guy Carbonneau said veteran David Aebischer would be back in goal against Toronto.
"Halak showed a lot of poise and handling the puck like he does behind the net helped our team, but David has the experience and we need him to be strong," said Carbonneau.
"David was a top goaltender at the start of the season and we'll need him in top form if we're going to be successful at the end of the season."
While injuries look to be clearing up, illness remains an issue in Montreal. Veterans Saku Koivu and Sergei Samsonov missed practice with the flu, although they are expected to play.
Carbonneau dismissed it as normal sickness that hits every club at this time of the year and said the players stayed home "as a precaution more than anything."
A nasty gastrointestinal virus ran through the team in late December, just as the team went into a slide from fourth in the conference to out of a playoff spot.
Then Rivet got pneumonia.
"That was a (virus) that hit this team like no other," Rivet said. "It was very tough on the body.
"Then jumping right back into playing and travelling, with the immune system not recovering and getting more colds, my body picked up something it couldn't fight off."
The Canadiens returned forward Duncan Milroy to AHL Hamilton. The fourth-year pro had an impressive five-game stay in Montreal, even if he was held to one assist.
Carbonneau lauded his energy and strong positional play.
"I proved to people who thought I was not going to be an NHLer and that I'd be a career AHL player that I have the will and desire to play in the NHL," said Milroy. "I think I did well up here.
"I've got five games under my belt now. I know what to expect. I know what I have to improve. I'll go to the AHL and work even harder now because I want to force their hand so they'll want me back up."
Carbonneau said rookie Guillaume Latendresse, whose play has slipped of late, would be back in the lineup after sitting out one game.