Neil Lennon's side claimed the SPL crown almost a month ago and advanced to the last-16 of the Champions League this season before being knocked out by Juventus.
Hibs stand in the way of further glory for the Hoops though and Mulgrew has promised they will not take them lightly.
"To get the double would be great and obviously we have had the Champions League as well," Mulgrew told Celtic View.
"Domestically, to win the league and the Scottish Cup - the two main trophies - would be brilliant.
"We have to beat Hibs first, though, and they will be up for it and we need to be ready for their threat.
"The cup final is always a good way to end the season, playing at Hampden, and it will obviously be even better if we win it.
"If we put our minds to it, are focused well and play well on the day we can win the game. We need to match them first and be up for it - that's the main thing."
Celtic have suffered Hampden heartbreak in recent seasons but Mulgrew remains confident of success.
"I suppose we have lost out in a few of the cups but we have done a lot of good things in that time as well," he added.
"It would be nice to win the Scottish Cup and round off this season.
"It was a good win for us against Dundee United in the semi-final. We had never bought into the Hampden hoodoo thing, and we just concentrated on our game."