Mark Bower wants to tie up a deal to stay at City - but has turned down their first offer.
The Bradford-born centre-half, who emerged as one of the biggest pluses of the last campaign, is hoping to agree a three-year contract before he flies off on holiday.
Bower said: "We are talking about it at the moment and should have something sorted very soon. There are just one or two things to arrange but I would be happy to sign.
"I've been very pleased with how the end of season went from a personal point of view. Having not played until the beginning of March it was a good chance to prove myself.
"It couldn't have come at a better time for me otherwise I could have been one of the thousand players looking for work in the summer. Even the First Division clubs are trimming down their squads so a lot of people are available on free transfers.
"There are going to be players struggling to get a new club. But hopefully I can sort out my future with Bradford."
Bantams boss Nicky Law said: "We've made Mark's agent an offer that hasn't been accepted at the moment."
Dundee United have slapped a £150,000 price tag on Alan Combe.
The Tannadice club have warned City they will not wait around forever to do a deal for the keeper, who was a big hit during his loan spell at Valley Parade.
Boss Alex Smith, who has been linked with a swap deal for Eoin Jess, said: "There has been an amount of interest in Alan and I mean to do business but it does not necessarily have to be with Bradford. They are keen to keep him but there are one or two others who may want him.
"I want something to happen for Alan as he was unlucky with the way things went for him here. He has had a taste of the English game at Bradford and that has whetted his appetite."
l Fans can pay on the day for Stuart McCall's testimonial match on Sunday providing they use the following turnstiles: Carlsberg Stand N13-14 for Rangers and Symphony S3-6 for City.
The Valley Parade ticket office will be open from 9am to 5pm on Saturday as well as before the game. The turnstiles will open at 1.30pm and with a crowd of over 20,000 expected, fans are urged to come early.
Admission is £10 for adults and £5 concessions.
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