City have rejected the first January bid for Nahki Wells.
The club confirmed that an offer has come in this week for their star striker – but they knocked it back.
The mystery bidders have not been identified but QPR, Wolves, Huddersfield and Blackburn have all been strongly linked with the 15-goal hitman.
There have also been a couple of inquiries from Premier League clubs.
Director of operations David Baldwin confirmed: “We’ve had one formal bid for the player. It is improved on what Peterborough offered in the summer but it’s not where the club want to be.
“There will possibly be other offers. But when they occur, the club will act accordingly on the information we receive.
“We can’t do more than that. But from a football perspective, Nahki continues to go out there and hopefully carry on scoring goals.
“Unless we see any other offers coming through, which we feel are worth considering, Nahki remains very much a Bradford City player and part of our plans.”
City turned down a seven-figure offer from Posh and speculation suggests they would be looking for £2m plus for Wells.
Baldwin insisted that there is no specific amount in mind but the club are wary that with 18 months of his contract left, the striker’s value will start to depreciate beyond the current transfer window.
He added: “When an offer comes in, it is discussed with the two chairmen and, as we stand, the first one is not something we want to accept.
“Contrary to message board comments, we aren’t going to put a specific price on his head. Football is very speculative as to values.
“We are not attaching a ‘for sale’ sign to the back of our player. That’s not what the club is about.
“Nahki Wells is obviously an integral part of this current team. He is also an asset to the football club and for the future stability of the football club.
“That asset element disappears by each transfer window. In the summer window, you are in danger of having a lesser value because he has less time on his contract.
“Come January 2015, he is able to sign a pre-contract for nothing.”
Phil Parkinson wants a cut-off point on the Wells scenario to ensure there is time to rework the squad if his main striker does move on.
Baldwin said: “I think anybody likes clear pathways, we all feel that way. Supporters want to know which direction it’s going, the manager does from a team selection point and the board need to know for financial planning and team requirement perspectives.
“We’re all in the same boat. But we’re all dictated by what a third-party club wants to do.
“At present, the only third-party club we’ve had contact with have made an offer that’s not acceptable. So there is no decision to make.
“When there is interest in the player, you have to react to that. But it is always a reactionary position from us.
“If you receive an offer, you have to make a decision as to what you’re going to do with the player based on what’s left on his contract.
“Let’s see what happens during the month. In the mean time let’s concentrate on what’s happening at our own club in terms of improving results on the pitch.”