The League One champions booked their place in the last four with a 2-0 replay victory over Albion Rovers while Jackie McNamara's United reached the semis with a 5-0 demolition of fellow Premiership side Inverness Caledonian Thistle.
United, who are flying high in the top flight of Scottish football, beat Rangers 3-0 in last year's competition but McCoist feels this season's encounter is too close to call.
Speaking from the John Hartson Foundation Golf Day at Loch Lomond, he told Sky Sports News: "Everyone will have different opinions on who will be favourites but the one thing I firmly believe is that I don't think favouritism will matter at all once the game starts.
"Different people at this moment in time will have different opinions. I've seen United in recent weeks and they are a very good side.
"They dismantled Inverness and came back and showed great spirit against St Mirren at the weekend and they have a lot of young talent and a lot of experience.
"I'm not sure who would be favourites but I don't think Jackie nor myself will be bothered about that."
And former Rangers goalkeeper Andy Goram is going one better than his old team-mate, claiming last year's League Two champions can go all the way in the tournament.
Speaking from the same event, he said: "I think we are a lot better equipped this season than we were last season.
"We have a far better squad and a stronger squad and when everyone is fit we are decent.
"I don't see why we can't win the Scottish Cup but we will have to step it up a gear from last night. You have to do that anyway when you play teams from a division above you."
Watch Rangers take on Dundee United at Ibrox Park live on Sky Sports 2 from 12.30pm on Saturday, April 12