The Light Blues boss saw his side book their place in the last 16 with a 3-0 win over Elgin yesterday as goals from Dean Shiels, Kevin Kyle and Kal Naismith saw off their Irn-Bru Third Division rivals.
Having already faced SPL sides Motherwell and Inverness Caley Thistle in knock-out action this term, the Ibrox crowd would relish the chance to take on another top-flight team. McCoist said: "I hope we are ready. I don't see why not.
"In the two League Cup games, we performed well against Motherwell and the first goal against Inverness was going to be vital, we didn't get it and then we didn't play well in the second half.
"But as I have said, it is not a crime to be beaten by Inverness this season, as a lot of people know.
"I wouldn't start screaming from the roof-tops that we are ready for anything but an SPL team wouldn't scare us."
Rangers' passage to the fifth round was never seriously in doubt at Ibrox yesterday, with the Light Blues controlling the tie from the off.
The man of the match champagne went to youngster Barrie McKay, however, and McCoist was delighted with him.
He said: "I thought McKay's performance was as consistent as he has been throughout a match.
"He has always shown flashes of good play and intelligence but I thought he consistently played well over the period of the game.
"One of the pleasant problems we are having when players are coming back from injury is picking a bench.
"Kal deserved it, he scored at East Stirling and he has been looking quite sharp and scoring in the reserve games so we kept him on the bench and I was delighted to see him get his goal."
There was a moment of concern for McCoist as Ian Black was forced off before the hour with a hyperextension of his knee.
The midfielder never recovered after a first-half knock and will be assessed today.
McCoist said: "He is struggling a bit. He overstretched after about 25 minutes and he went on until half-time.
"The doc had a look at him and he said he wanted to go out and try it. He is struggling a bit but we will assess him.
"At this early stage, it looks like it might be a couple of weeks but we will see."