The two sides meet with Motherwell currently top of the SPL, having gone unbeaten throughout the season, while the Gers are also yet to be defeated this season and are top of the Scottish Third Division.
McCoist told reporters: "I think [Motherwell manager] Stuart [McCall] and I will probably disagree on this but I would have to say Motherwell, being top of the SPL, are favourites.
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“The fact we are going through a transitional period and we’ve a completely new team adds to that.
“But that aside, favourites can get beaten and I believe we can beat Motherwell. Of course I do. We’ll be doing our damnedest to do that.
“The cup competitions provide an ideal situation for us to gauge how we are placed when we play against the top teams in the country.
“We’re doing that this week and it will give us an indication of where we are. It won’t be the end of the world if we don’t win the tie but I firmly believe we can.
“They will fancy their chances against anybody at this moment in time. They are extremely well organised and have got flair players.
“Motherwell always gave us very hard games when we had £25-30million worth of talent in our side.
“Things certainly won’t change in that respect and they will give our new team a very tough night.”