Free agent Barrie McKay is training with Livingston and could be offered a contract after the Premiership strugglers lost Scott Arfield and Connor McLennan to injury.
Former Rangers playmaker McKay, 31, has been without a club since leaving Hearts last summer.
Manager Marvin Bartley refused to be drawn on interest in McKay but did confirm that veteran midfielder Arfield and winger McLennan are facing spells on the sidelines with hamstring and ankle injuries respectively.
"I don't think they'll be back for the next couple of weeks, put it that way," he said.
"I think Connor will be slightly longer than Scottie is, but definitely not for the next couple of weeks.
"It's a massive blow. We're down in numbers in terms of the size of the squad as well, so losing any players at this moment in time makes it extremely difficult, especially those two players.
"Connor's done extremely well for us and obviously Scottie was brought in (in January) to give us that boost in attacking areas.
"We've lost two boys from the top end of the pitch, but it's an opportunity for others to now step up and go into the team and take their places."
Bottom side Livi visit third-placed Celtic on Wednesday bidding to end a 25-game run without victory.
"It's a massive task, isn't it?" said Bartley. "Celtic are obviously chasing another title. It'll be extremely difficult.
"On any given day, anything can happen. If you go into football thinking you can't win, then it would be pointless."