The storied Edinburgh club, who have won the Scottish league title four times and were the first British club to enter European competition, have not tasted success in the national showpiece since 1902.
They have reached the final twice in the last three years – losing to Hearts and Celtic respectively – but, speaking ahead of Saturday’s Sky LIve semi-final with Falkirk, Stubbs is convinced their luck is bound to change.
He told Sky Sports News HQ: “I’m very aware of what has been going on in the Cup with the history of the club. They have gone close in recent years but not close enough.
“It will change, it is just a matter of time. Whether it is this year or not, only time will tell, but it will change one year.”
Hibs and Falkirk have met three times in the Championship this season but the Edinburgh side have yet to record a victory after two draws and one defeat.
Stubbs said: “It’s obviously very exciting and the players are really looking forward to it. We know it’s a big game.
“I’ll let people make their own assessment of who they think is favourite on Saturday. All I’m doing is focusing on my own team; I know if we play well we can get a result.
“The games have been very close and we have actually performed well in two of them. But this game is different because it is the semi-final of the cup and so it’s a nice little break form the league and it’s one that we are all really looking forward to.
“The league is very important because we want to get back up to the Premiership as quickly as possible but the cup is important too. We want to have success in both.
“It all helps if we get to the cup final because of the extra finance that becomes available and hopefully I will see some of that. The fact that we are in this stage of the season and we are fighting for silverware and promotion, that is the important thing.”
Watch Hibernian tackle Falkirk in the Scottish Cup semi-final on Saturday 18 April on Sky Sports 2 HD from 12.15pm