On Sunday, Phil Parkinson's League Two side will become the first fourth-tier team to contest a League Cup final in more than half a century when they take on Michael Laudrup's Swans at Wembley.
But Bantams co-chairman Mark Lawn has revealed the west Yorkshire outfit may turn down the opportunity to compete in Europe next term if doing so would cost the club money.
Quoted in The Sun, he said: "I'm not going to pay to play in Europe.
"When we beat Villa (in the semi-final), I was told, 'You don't really want to get into Europe - it costs you money in the early rounds'.
"I said, 'Well, that'll be fun because if it costs us money, we won't be there'.
"Realistically, it's not going to be a problem because I don't think we're going to win against Swansea."
He added: "I won't put us in fiscal danger to play in Europe. That's not going to happen. I'm deadly serious.
"It's all very well saying there are financial rewards once you get to the group stage.
"But we're a fourth division club - realistically, we're not going to get there."