Both Gough and Celtic's McStay missed out on Saturday as Celtic closed the gap between the two sides to five points - their 2-0 win over Hearts, with goals from Jorge Cadete and Paolo Di Canio, shading Rangers' 2-2 draw against Aberdeen.
McStay was injured against Hibernian last week, while his fellow midfielder Peter Grant and right-back Jackie McNamara are also fitness concerns.
Rangers will be without both Sebastian Rozental and Paul Gascoigne on Thursday, while Gascoigne is also doubtful for the crucial League fixture in a fortnight's time as he tries to shake off an ankle injury.
Gough missed Saturday's draw at Aberdeen with a calf strain but should be fit for Thursday.
The arrival from Milan of Enrico Annoni, the tough Italian defender, has heightened expectations in the Celtic camp that they can come out on top on Thursday, although victory has eluded them in the last nine fixtures between the sides.
Annoni, who made his debut on Saturday, is seen as a defender who can shackle Brian Laudrup, who has played well against Celtic in the past - and, in the absence of the injured Paul Gascoigne, Celtic believe the psychological advantage of a Cup win can be theirs.
The Cup tie is followed in a fortnight's time by a League encounter crucial to Celtic's hopes of ending the Ibrox hegemony. "This is the most important spell I have faced as a manager," Celtic's Tommy Burns said. "In the last two seasons, the psychological boost Rangers have taken from winning these games was there for all to see. If we were to win both games it would blow the season wide open."
The success of Rangers in recent seasons, however, has been based as much on their ability to come out on top in crunch games as their consistency in grinding out results - and in Laudrup they have a potential match-winner. The Dane was on target after five minutes against Aberdeen but the Dons came back through Toni Kombouare and an Andy Goram own goal before Craig Moore rescued the point.
Dundee United stretched their unbeaten run to 13 games with a 2-1 win over Dunfermline, a result which keeps them comfortably in third place.