A home game against Albion Rovers is all that stands in the way of Rangers reaching the semi-finals, which will both be held at Ibrox.
The League One leaders are second favourites behind Aberdeen with all the major bookmakers after the Dons were handed a home tie against Dumbarton as reward for their shock win over holders Celtic.
But the Rangers boss believes there is little difference between his side and the Scottish Premiership teams left in the tournament. St Johnstone face Raith Rovers away after their 4-0 win at Forfar while Dundee United are set for a trip to Inverness if Caley Thistle can overcome Stranraer in a replay.
McCoist : "Some bookies might have us as favourites now as is their right but I wouldn't go that far.
"I'm not trying to play any mind games when I say this but I think Aberdeen and Dundee United will, in a lot of people's eyes, still have a slightly better chance.
"I counted us in the next band after Celtic and I still do. I don't think there's an awful lot between a lot of the teams there.
"But United beat St Mirren 2-1 and I watched St Johnstone three weeks ago when they beat Partick 1-0 and they weren't looking bad at all.
"You've got to say they had a fantastic result at Forfar and a lot of people would have been looking at that as a really tough fixture.
"We're in the mix but when you consider the other teams in there, I still don't think we're favourites to win the competition. I genuinely don't.
"You'd have to say Aberdeen, having knocked the holders and the champions out, would probably be most people's favourites now."