The 33-year-old, one of City's higher earners who arrived on a free transfer from Mansfield last summer, was among those expected to leave after manager Stuart McCall's budget was slashed by a third.
But Boulding told the club's official website: "I have talked to Stuart and have said I would be prepared to take a cut. We just need to sit down and talk about it.
"It's difficult for me to say too much, but I don't want to leave Bradford. As long as the club still want me, then I want to be here.
"I don't want to stay and sit around just picking up wages because that's no good to anybody. There's been no talk about walking away from the club. I don't want to because it's a great place to be and, for me, there's a lot of unfinished business."
Boulding scored 13 goals as the Bantams lost out on a play-off place last season - half the tally he chalked up the previous year with relegated Mansfield.