The Pittodrie outfit will face Inverness at Celtic Park on March 16 hoping to land their first trophy since 1995 after thrashing St Johnstone 4-0 in last Saturday's semi-final.
But before that, they have the chance to take a giant step towards a second tournament win when they face holders Celtic in the fifth round of the William Hill Scottish Cup at Parkhead.
And Considine claims that the prospect of one trophy success has only made Derek McInnes' side hungry for more.
Speaking ahead of Saturday's match, the 26-year-old told RedTV: "It's worked out quite well after last weekend's game. Going into the Celtic match we are high in confidence.
"I would say it's going to be our hardest game of the year so far. They are going to be well up for it.
"But there's nothing wrong with being a bit greedy and wanting Aberdeen to continue in the Scottish Cup. The boys are flying and thoroughly looking forward to it."
It is six years since Aberdeen beat the Hoops in Glasgow but confident Considine believes this Dons side can end that long wait.
"Celtic are massive favourites for this game but I think we've shown each time we've gone down that it's going to be an entertaining game. There have been a few last-minute goals, plenty of goals and we went down there in the Scottish Cup and beat them a few years back. There's no reason why we can't do it again.
"You know Celtic will have the majority of the ball but I feel on the counter-attack we are dangerous and we've got boys who can score goals and we've just got to go down there and give it our best shot.
"Obviously going back a good few years ago we were going to Celtic Park without expecting to get much from the game - I think most teams were - but I think with the amount of experience we've got in the squad now we can go down there with real confidence."