But McCoist knows they will first need to stand up to whatever League One rivals Dunfermline throw at them following a bruising encounter on their last visit.
The former Scotland striker is looking to improve on a disappointing cup record as Rangers host the Pars in their fifth-round tie on Friday night.
McCoist has only reached one quarter-final in five previous attempts in Scotland's two main cup tournaments, although his team have a Ramsdens Cup final against Raith Rovers to look forward to in April.
With the Gers 23 points ahead of Dunfermline in the league, a cup run is the main point of interest for the Light Blues fans.
"I don't know if it takes on greater significance, it certainly has massive significance," McCoist said. "Obviously last year wasn't good for us, we had a disappointing result at Tannadice.
"It would be good for the supporters and the players. You need a bit of luck to go on a cup run and we certainly need that, but we certainly believe we've got players who can go on a cup run.
"We have got a bit of experience in the squad with lads who have had success in cup competitions, obviously Lee McCulloch in particular but also (Ian) Black, (Jon) Daly, Cammy Bell and people like that.
"We believe, outwith Celtic, who would be most people's if not everybody's favourites to win domestic competitions because of their strength at this moment, we believe we are on a par with the rest of the SPL teams. Aberdeen are obviously very strong as well.
"But we are looking forward to the tie and nothing more than an opportunity to extend our run."
Rangers endured a difficult evening when Dunfermline last visited Ibrox, on league duty in November, with Bilel Mohsni's 90th-minute goal securing a 3-1 win against 10 men.
But it proved a costly three points with Andy Little suffering a broken jaw and cheekbone, Mohsni breaking his nose, Richard Foster ruled out for six weeks with an ankle injury, and McCulloch needing six stitches in a head wound.
"We ended up with four players in hospital," McCoist said. "But it was a hard, fair game. I sometimes criticise players not being allowed to tackle like we used to in older days.
"I think the physical side of the game is something that should never be taken away from football. It's part and parcel of football."
McCoist, whose team won 4-0 at Dunfermline in December, added: "I think possibly Dunfermline caught us on the hop a bit with their natural aggression to play the game at Ibrox.
"We don't in any shape or form have a problem with that.
"We did well to see that game out and win the game, but I thought in the game at East End (Park) we were ready for any eventuality that was thrown at us and I would be very hopeful that will be the same again."
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