City want to beat the deadline by making one more signing before the transfer window slams shut.
But they refuse to be held to ransom as rivals sense there is more money to be had from the Capital One Cup kitty.
The Bantams have made a bid for an unnamed player and hope to get it done before time runs out at 11pm tomorrow.
His club, though, have dug their heels in for a bigger fee – something that City will not match.
Joint-chairman Mark Lawn said: “We are trying to get another player in before the deadline but unfortunately their valuation and our valuation do not match at present.
“It could be an aspect that other clubs have seen what we’ve done in the cup and think they can demand more money. But we won’t be paying what we think is over the odds.”
Phil Parkinson has made three January signings so far – Michael Nelson for £30,000 from Kilmarnock, Andy Gray and Southampton left back Ryan Dickson on loan for the rest of the season.
City are keeping the identity of their latest target under wraps but an attack-minded midfielder has been on the radar.
Rumours have persisted throughout the month about top scorer Nahki Wells, with Leeds, Huddersfield and Wolves among those believed to be watching him. But Lawn stressed once again that there has been no interest registered.
He said: “We’ve had no firm bids or even requests from any football team. Nobody has approached anyone. It’s only the agent that’s been making noises.”
City fly back into Manchester from Tenerife tonight after a four-day break which Parkinson believes will revitalise his squad ahead of the next run of league games and Wembley.
The Bantams boss said: “It’s been a tremendous trip. The lads had a little bit of down time on the first day and the training facilities are first class.
“We’ve been able to utilise the swimming pool and a really good pitch. It’s been great for Andrew Davies and Luke Oliver as well.”
Davies is aiming to make a late bid for the Capital One Cup final and Parkinson felt the trip has really helped the big defender’s progress.
He said: “Andrew’s at the stage (of his recovery) where he is starting running and being able to do it on a good surface every day has been really beneficial for him.
“Back at home you’ve got the hard conditions and running on artificial turf is obviously tough on his knee. It’s been important to get him working on a good grass surface.”