The 34-year-old has not played since January 5 after being troubled by the persistent injury.
McCoist told his club's official website: "I got a report from our physio Pip Yeates today and the good news is that Lee is making steady progress.
"I would be very hopeful that our captain would be involved in the weekend and it follows that Lee would be very keen to play.
"We will monitor him and we will be in a better position to make a judgement later in the week.
"It's safe to say that having the captain in our side at Tannadice would be great. Lee obviously has a lot of experience all over Europe and in the UK and he is a player we would love to have with us at the weekend."
- Sports & Recreation