Luke Medley has rejected the chance to stay at Valley Parade.
The young striker is understood to have verbally turned down the one-year offer on the table from City.
He has until Saturday to put it in writing before the three-week deadline is up and the deal is withdrawn. But he is thought to be looking for somewhere nearer to his London roots.
Medley, 19 later this month, scored twice last season - including a sensational volley against Wrexham in August with his first touch to clinch Stuart McCall's opening win in charge.
His other goal came from the penalty spot at Wycombe on the final day of the season on his only start.
Medley, who joined City after a successful trial when David Wetherall was in temporary charge, made eight appearances from the bench. He also had a brief loan spell with non-league Cambridge City.
Because of his age, City would be entitled to a small compensation fee if Medley signs for another club as they have made him a contract offer.
Medley's departure leaves McCall with last season's top scorer Peter Thorne, Barry Conlon and Willy Topp as his attacking options.
He is in the market for at least one new striker and talks have taken place with Huddersfield's Luke Beckett.
Michael Boulding, who has left Mansfield, and Halifax's John Shaw have also been linked with Valley Parade. Meanwhile, the club's season-ticket push could be swelled by an unexpected source - Halifax Town fans.
A local businessman has come up with a financial incentive to persuade Shaymen followers to take in matches at Valley Parade as well as watching their own team.
City fan Glenn Ackroyd, whose property firm A Quick Sale is based in Halifax, is offering to cough up £51 towards the cost of a season-ticket for any Town supporter - leaving them £99 to pay.
Joint-chairman Mark Lawn said: "Glenn isn't trying to turn anyone into Bradford City fans by doing this. But he wants to give them the chance to see some league football as well as watching Halifax and enjoy the best of both worlds.
"It's a genuine offer from Glenn. All they have to do is bring proof of ID to the ticket office with two utility bills showing a Halifax post-code and they can purchase a season-ticket for £99. Obviously this does not apply to any Bradford City fan who lives in that area. We have quite a few on our database with Halifax post-codes."
The Valley Parade box office is open from 9am to 5pm Monday to Saturday and 10-4pm on Sundays leading up to the half-price deadline on June 15.
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