Bruce's side travel to face Cardiff in the Premier League on Saturday before taking on Brighton at the KC Stadium in their FA Cup fifth-round replay on Monday.
The winners will then host Sunderland in the quarter-finals and Bruce insists he is not concerned at the prospect of having to squeeze more fixtures into an already busy calendar.
"The Premier League is the most important thing but if you are edging towards a date at Wembley, whether it's a semi-final or a final, that would be terrific too," he said ahead of the league game at the Cardiff City Stadium.
"We are not exactly steeped in the history and tradition of going to FA Cup finals and semi-finals, so it would be terrific for everybody concerned.
"Why can't we mount a challenge on two (fronts)? I have seen all this nonsense about fixture pile-ups.
"It's a game of football and if you get to this stage and you have got a replay to get into the quarter-final of the cup and a home game in the quarter-final, then there is all to play for."
However, Bruce did admit that injuries to his players was a concern in such a demanding run of fixtures.
"It's not easy playing Saturday, Monday; I think that's ridiculous," he added.
"It baffles me. Footballers could play every day but they can't play with the same intensity.
"It's like asking an athlete to run a race and then do it again the next day in the same time. It won't happen.
"The thing you have to guard against, that we all worry about, is if you play more games you pick up injuries.
"Very rarely does it happen in training, most of them come taking part in games. If you put your first 11 out and lose two or three of them for the run in, you've got problems."