Stephen Kelly and Damien Johnson have both returned to light training.
Kelly has missed Blues' last three games because of a thigh injury and club captain Johnson has not played at all this season because of a back injury.
"Kells actually did a bit of light running yesterday, so he'll start picking it up of next week," said first team coach Roy Aitken.
"I would have thought by the middle to the end of next week he'll start joining in again.
"Whether he'll be ready for Burnley I think will be a long shot, but we'll see how he is.
"Damien is now at the stage where he's back running and his progress is good.
"Between the physio, the medical specialists and himself they'll decide when he comes back in.
"He's now doing the aerobic type running which he has not got a problem with anyway because he's got a great level of fitness.
"The main thing is that there is no reoccurrence of the back problem.
"The good thing is that he's training so that's a big plus."