Rangers are amid their best run of form this season, having won their last five league and Scottish Cup games, scoring 20 times and conceding just two goals.
Yet McCoist believes the match at Montrose’s Links Park will provide a stern test, especially with bitterly cold weather predicted, as well as a packed-out home attendance.
McCoist said: “I’m expecting another tough away game. We saw in midweek how tough it is for big clubs going to supposedly smaller venues.
“Montrose have been doing well and we’ve had a couple of good reports on them. They won 4-1 at Berwick last time out.
“They’re undefeated in a few games and they’ll fancy their chances with it being a home game but it’s an opportunity for us to extend our lead in the league.
“I think with the weather and the game being live on television, all the ingredients are there for a cup tie atmosphere if you like.”