Celtic won the League Cup last season on their way to doing the domestic double.
The Bhoys triumphed in the competition during the 2014/15 campaign, but Mackay-Steven was not able to play his part after moving to Parkhead.
The winger was cup-tied after joining Celtic in January 2015, having played in the tournament for his previous club Dundee United earlier in that season.
And the Scotland international attacker said: “Trophies are what every player wants to win and I’m desperate to win this cup,” he said. “I’ve never won it before so it’s a massive thing for me.
“We’re in the quarter-finals now and we’ve got a big tie to look forward to against Hearts but we’re one game away from playing at Hampden and that’s a special feeling."
The League Cup was the first trophy that Ronny Deila won at Celtic, so it will always have a special place in the Norwegian manager's heart.
The Bhoys' route into the semi-final is far from guaranteed though, as they face a tough test against Hearts in the next round.
Hearts have made a promising start to the campaign, and they sit in third place in the league, so Wednesday night's fixture looks a tough test for Deila's men.
Celtic will go into the game with confidence though, as they have been unbeaten in their last six domestic matches and have taken a commanding lead at the top of the Scottish Premiership.