He was substituted in the first half of yesterday's 3-0 win against Clyde.
However, the good news for Gers manager Ally McCoist is the 13-goal hitman's hamstring injury is not serious and his departure was merely a precaution.
The Northern Ireland internationalist came off after just 25 minutes of the 3-0 victory over the Bully Wee, shortly after Lee Wallace had scored the opening goal.
He was a concern for McCoist at the time, but afterwards the boss revealed it was only tightness rather than anything more sinister that forced Little to come off early.
Lewis Macleod is another player who needed treatment on the pitch. He was replaced during the recent 6-2 win at Elgin.
But despite taking a couple of knocks in the last few days, McCoist expects Macleod will be fit enough for Hampden.
The manager told the Rangers website: "Andy's got a tight hamstring and we'll reassess it today when he comes in for treatment.
"I would have to say with my knowledge of hamstrings that he is probably going to be a doubt for the weekend.
"Lewis is fine though. He took a couple of whacks yesterday and got an accidental elbow in the face but he's okay.
"If we do lose people we've got others waiting to come in and there's competition for places now which is healthy.
"Ian Black has been back in for a couple of days of training again and Dean Shiels came on as a substitute for Andy."