The Kings (15-28), one-half game ahead of Western Conference-worst Utah (15-29), have played the last two contests without Cousins (ankle sprain) and Gay (Achilles strain), who combine for 42.7 points per game.
Sacramento, though, nearly pulled off an upset in Friday's 116-111 overtime loss to Indiana before falling 125-117 to Denver on Sunday. Isaiah Thomas scored 22 points for the Kings, who are hoping to have at least one of their top players back Monday.
Coach Mike Malone said before Sunday's contest that Gay is closer to returning than Cousins, though both will be evaluated before each contest to determine their availability.
"The reality is if DeMarcus and Rudy are out, other guys have to step up," Malone said. "We had six guys in double figures and we're going to need that again (Monday). Utah is waiting on us, it's a very tough place to play and we're going to have to have a concerted team effort to have a chance to win on the road."
The Jazz lost back-to-back games to Minnesota before beating Washington 104-101 on Saturday behind a solid performance from reserve Enes Kanter, who scored 24 points and hit 11 of 13 from the field.
Derrick Favors played after missing the previous contest with a right hip strain and finished with 11 points and 14 rebounds, but he deferred to Kanter most of the night.
"Enes was doing the scoring, so I just tried to go out there and play defense and get rebounds," Favors said
Kanter scored four points in each loss to the Timberwolves.
"I personally was really bad two games against Minnesota, (so) I wanted to come out with lots of energy," Kanter said. "My coaches have given me a lot of confidence and we've been practicing really hard. The things I have been trying to do and now showing in the games."
"We did a good job of attacking them after playing inside-out," said Burke, who had 12 points and eight assists. "We attacked them in transition, attacked them in the half court."
Jefferson scored 20 points, while Favors and Hayward had 17 apiece to help Utah beat Sacramento 122-101 in the last meeting Dec. 11.
Thomas had 20 for the Kings in that contest after scoring 26 off the bench Dec. 7 to help overcome Hayward's 22 points in a 112-102 overtime victory. McLemore hit a 3-pointer with three seconds remaining in regulation to send it into OT.