Martin missed training on Thursday while Murphy sat out last weekend’s victory over Falkirk after suffering a foot knock.
Left-backs Declan John and Lee Wallace are also fighting to return to fitness.
Murty said: “Russell felt a disruption in his back and we have de-loaded him, we are going to see how he goes with a bit of treatment.
“Jamie will be the same, we will give them both the maximum time possible to see how comfortable they are feeling and make our selection from there.
“We will make our decision as late as possible to give all the guys enough time to feel really fresh for a big game.”