Rovers’ Group B campaign in the newly named Premier Sports Cup sees them visit Cowdenbeath this Saturday (KO 3pm) before hosting Brechin City next Tuesday (KO 7.45pm) in a group also containing Livingston and Alloa Athletic.
The eight group winners and three best runners-up will join Scotland’s five European representatives in the knockout stages.
"On paper it’s as good a chance as we’ve had to qualify in the last umpteen years,” McGlynn said. “We might not necessarily win the group but that second place could be up for grabs.
"The league is the priority but this is something that can kickstart our season if we get through this.
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"Momentum is very important in football and if you get it in the League Cup you can take it into your league campaign and that’s what we plan to do.
"Winning football matches breeds confidence, it breeds the feelgood factor and gives everyone inspiration.”
McGlynn, who is keen to sign a striker and a central midfielder, has revealed that centre back Dave McKay is at last available to play competitively again for the first time in 16 months after coming through a low-key bounce game on Monday.
The gaffer reckons this Saturday’s trip to Central Park represents a tricky opener.
"Cowdenbeath is a difficult game of course,” he said. “It’s a derby away from home.
"We had them in our group last year and we managed to win a scrappy game 1-0 in late November on a horrible windy day.
"We’re playing them at a better time of year this time so we hope conditions are better for producing good football.
"But Gary Bollan’s been building a team at Cowdenbeath. Two or three years ago they were in the play-offs for trying to stay in the league and for a couple of years it was very nervy.
"But Gary’s steadied the ship and they’ve not been in that situation the last two years.
"They will certainly be competitive at the top end of League 2 this year and on their day they’ll give anyone a hard game at Central Park.”