Brechin were the Ibrox outfit's first opponents following their liquidation and demotion to the bottom rung of Scottish football in July 2012.
They were forced into extra-time by the Hedgemen in that Ramsdens Cup first-round tie before securing a 2-1 win.
The new League One champions now return to Angus for the second time this season after they were given another scare back in October when they had to rally from two goals down to win 4-3.
McCoist said: "We're going back up to where it all started for us. We played Brechin in the Ramsdens Cup at the beginning of last season.
"It's a special place for Rangers now and the guys up there have been great to us. Their chairman Ken Ferguson and the others who run the club are fantastic but once the first whistle goes it will be different.
"We saw that the last time we were up there. Dearie me, it was an incredible game and it will be the same this time."
Rangers have stormed to the League One title without losing a game, but McCoist knows they will have to step up performances next term if they want to escape the Championship at the first attempt.
He said: "We are stronger than we were last year but then again, we will have to improve again if we want to get ourselves back up the leagues."