The goalie was injured in the first period of a 3-2 shootout loss to the Boston Bruins on Tuesday after making three saves. He was replaced by Dustin Tokarski.
"Ullmark is a more challenging one right now because it's week to week, and you look at the number of weeks left in our season," Sabres coach Don Granato said Friday. "So that one is, I'll follow up with you on it, but right now it's week to week and we don't have many weeks left. So that one's a little touchy."
Tokarski made 27 saves for his first NHL win since 2015 in a 5-2 victory against the Washington Capitals on Thursday and is expected to start against the Pittsburgh Penguins on Saturday (3 p.m. ET; NBC). He is 1-4-2 with a 3.32 goals-against average and a .908 save percentage in seven games this season.
The Sabres also are without goalie Carter Hutton, who hasn't played since March 22 because of a lower-body injury. Ullmark and Hutton can each become an unrestricted free agent after the season.
"Hutton
could be recalled. Luukkonen, who has not made his NHL debut, is 7-5-2 with a 3.60 GAA and an .888 save percentage in 14 games with Rochester of the American Hockey League this season. Michael Houser, who was the Sabres backup Thursday, also has not played in the NHL.
"There's going to be a determination on him later today where he will be integrated with us, but we're clearly trying to get him integrated with us," Granato said of Luukkonen. "Now it's a matter of, I guess he hasn't been on the ice much in Rochester is my understanding, so today's an important day to determine when he'll be integrated with us. That information will come with the other stuff later today."
Buffalo (11-25-7) is last in the eight-team MassMutual East Division, 23 points behind the fourth-place Boston Bruins. The top four teams in the division will qualify for the Stanley Cup Playoffs.
NHL.com independent correspondent Heather Engel contributed to this report
