Coach Lindy Ruff said Monday he didn't know whether either will be healthy enough to play before the NHL playoffs open next week.
"They're both doing a lot better," Ruff said. "I'm optimistic we'll get them back on the ice maybe later in the week. Whether they'll be able to play or not, I don't know."
Ruff said he'd prefer to have both play at least once before the playoffs to be conditioned to game action. The Northeast Division-leading Sabres have four games left, and close their season at New Jersey on Sunday.
Vanek has missed four games with a lower body injury. He skated briefly on his own before practice Monday. Connolly has missed five games with an injured foot, and has been limited to riding a stationary bike.
Connolly, the team's top play-making center, leads Buffalo with 65 points (17 goals, 48 assists) in 73 games. Vanek is tied for second on the team with 23 goals, and is fourth with 48 points in 69 games.
Gritty third-line forward Patrick Kaleta resumed skating on Monday, a week since having surgery to repair a thumb injury. But he's still not cleared for contact.
The Sabres (43-25-10) are coming off two straight losses in preparing to close their home schedule against the New York Rangers on Tuesday.
The Sabres are one win or one Ottawa regulation loss from clinching the division title. With 96 points, they're also a point behind the Atlantic Division-leading Devils in the race to finish second in the Eastern Conference.
Another incentive for Ruff is for the Sabres to play the role of spoilers, after Buffalo had its playoff hopes dashed in the final week of each of the past two seasons.
"We want to break some teams' hearts, ruin a few dreams on the way because we know how tough it was last year going down the stretch," Ruff said. "And we don't want anybody getting any gimmes off us."
The Rangers and the Boston Bruins -- whom the Sabres play Thursday -- are in a tight race for the East's eighth and final playoff spot.