Hull manager Bruce, who was in charge of Huddersfield between 1999 and 2000, led his current side to the Premier League last season and has seen his team pick up seven points from their opening five games after wins over Norwich City and Newcastle United, as well as a 1-1 draw with Cardiff City.
Following Saturday's 3-2 win at Newcastle, Bruce confirmed that he would make changes to the team for the visit of Huddersfield as he looks to prioritise Premier League survival.
"Well, we're in the cup competition, and of course it's a priority, but it's not a priority for us," he admitted.
"We've got two wins on the board and we need another eight to keep us in the division in my opinion."
Bruce also confirmed that central defender James Chester will be out for a number of weeks after he came off towards the end of the game at St James' Park.
"The big thing for me is can we keep injury free with our big players we've got?" he added.
"We've lost our centre-back for what looks like a few weeks and that could be the critical thing. He came off at the end and left us with 10 men, but there you have it."
City, who have never progressed beyond the fourth round of the competition, managed to seal their place in the draw after Robbie Brady's extra-time goal handed them a 1-0 win at League One high-flyers Leyton Orient in August.
Huddersfield's best effort in the competition ended in semi-final defeat in 1968 and victory on Tuesday would see them reach the fourth round for the first time since the 1999-2000 season, when Bruce was in charge.
Town have enjoyed a strong start to the campaign under boss Mark Robins, having narrowly avoided relegation back to League One on the final day of last season.
Robins has guided the team to three wins and three draws from their opening eight fixtures, a run of results that sees them lie in ninth in the Championship, just three points off the play-off places.
The game will represent Huddersfield's second Yorkshire derby of the competition already, having seen off Bradford City 2-1 at home in the opening round.
James Vaughan scored twice in that game and the former Everton and Norwich City striker has enjoyed a superb run of form this season, having found the net nine times in all competitions.
Seven of those have come in the league to make him the Championship's top scorer, but his goalscoring exploits were not required in the previous round, as Joel Lynch, Jonathan Hogg and Adam Hammill all found the net in a 3-2 win over Charlton Athletic.
