Tavernier (knee) has an outside chance of facing Celtic the following weekend while Jack (calf) is awaiting a fresh prognosis following trips to see specialists.
Defender Niko Katic (knee) remains a long-term absentee.
Hibernian's Steven Bradley is still struggling with a thigh injury.
Loan attacker Jamie Murphy is out with a recurring hamstring injury but would be unable to play against his parent club.
Sean Mackie remains out with a thigh injury.