First up is the fifth defence of his World Boxing Council belt against tough Australian Sakio Bika (32-6-3) on Saturday afternoon at the Pepsi Colisee. The bout will be televised as part of a new boxing series on U.S. network CBS.
Kovalev, coming off a one-sided stoppage of Montreal's Jean Pascal last month, holds the International Boxing Federation, World Boxing Association and World Boxing Organization titles. He's expected to meet Stevenson later this year to decide who's best in the 175-pound division.
Stevenson (25-1), a devastating left-handed knockout puncher who is also the linear light heavyweight champion, is aware of what's ahead but knows, for now, he must focus on Bika.
"I know Bika is very dangerous," the 37-year-old Montreal fighter said this week. "I know he's going to come into the ring and try to give me trouble.
"I'd love to unify the belts eventually, but I'll let my manager Al Haymon take care of that."
At the weigh-in Friday, Stevenson came in at 174.4 but Bika was overweight at 175.8. He had work off the excess and return later to make the limit at 174.6.
Bika lost the WBC super-middleweight (168-pound) belt to American Anthony Dirrell in his last bout in August. He will move up a weight class to face Stevenson, also a former super-middleweight.
"I made the move from 168 to 175 pounds and it worked well for me," said Stevenson. "I expect him to bring his best at 175 pounds.
"He's a former champ so I'm preparing to face a champion. I'm looking for the KO because I'm from the Kronk Gym. Knockouts sell. But I can go 12 rounds, that's not a problem. I train for 12 rounds."
Bika has never been stopped but may have never faced a power puncher quite like Stevenson.
"I want to test the big boy and I feel like I can do that," the Cameroon native said. "He's knocked people out but I've never been knocked out.
"I'll be the one to knock him out."
Bika was miffed at a news conference this week when reporters asked Stevenson about Kovalev. He feels the champion maybe looking past him.
"He's nervous," said Bika. "He's under pressure.
"I don't know if he can stand up to my power and pressure."
Stevenson won the title with a first-round knockout of Chad Dawson in 2013. He will fight in Quebec City for the third time in his last four outings. He stopped Dmitry Sukhotsky in five rounds there in December.
The co-feature has another light heavyweight bout with Montreal-based Russian Artur Beterbiev (7-0) against former WBA champion Gabriel Campillo (25-6-1) of Spain. The winner gets ranked as the No. 2 contender by the IBF.
Beterbiev, 30, who is being fast-tracked toward a world title shot, is coming off a second-round win over previously unbeaten Jeff Page in December.
His trainer Marc Ramsay called the Campillo bout an important test.
"Campillo is a complicated opponent, big, experienced and above all, a former world champion," said Ramsay. "He has a reputation as a prospect killer.
"He destroyed false prospects. It will give us the clues needed to find out where Artur is in his progression."
Another bout has welterweight Kevin Bizier (23-2) against Frenchman Faoud El Massoudi (12-4). It is Quebec City native Bizier's first fight since a close loss in December to Montreal's Jo Jo Dan.