The council, as landlord to the ground, confirmed that such an inquiry is not on the foreseeable schedule of its overview and scrutiny committee.
Cllr Sebastian Bowen, committee chairman, said an inquiry has not been dismissed but put off on legal advice given the club's uncertain future.
"It may be that the time for an inquiry will come once the dust has settled," he said.
Cllr Jim Kenyon, who called for the hearing, said an inquiry into the way the leases were re-assigned should happen "sooner rather than later."
Meantime, more nneded to be made public about payment plans that wre the basis of assurances made to the council by the clubs new owners, he said.
The call for an inquiry came in tandem with pressure on the council to release a report into due diligence it carried out on Hereford United ahead of leases being re-assigned five years ago.
The council’s Independent group is pushing for the report to be released amid doubt that it actually exists.
Independent leader Cllr Bob Matthews raised the issue of due diligence when group leaders were given an update on the council and the club last month.
Cllr Jim Knipe first put the issue to council leader Cllr Tony Johnson in an e-mail sent in April last year.
Cllr Knipe says he is “disappointed and alarmed” that, on the evidence so far, the council failed to carry out carry out a due diligence examination to establish the club’s financial position before negotiations over the leases began.
“Due diligence was not carried prior to the leases being renegotiated - if it was can they let us have sight off the report," he said.
In a statement the council said it carried out the “appropriate level” of due diligence when restructuring the leases - as it would with any existing long term tenant who was not a new entity.
The statement said the council was aware of the situation the club faced as was “endeavouring to help them where possible.”
While the council is the landlord of the Edgar Street ground, it does not have any direct control or involvement in the club and its decisions.
Two leases refer to redevelopment of the Meadow End and Blackfriars End and stipulate that any proceeds be re-invested in the ground and its facilities.
The council is considering a request by the new owners for a transfer of those leases to a holding company within their ownership.
Around £65k in rent arrears, business rates and legal fees is owed to the council by the club.
The council has accepted assurances from the new owners that all outstanding monies will be fully re-paid – with an agreement to a written undertaking.
As renegotiated, the leases on the ground continue to be held by the club. If the club folds the leases would revert back to the council.
Assigning the Edgar Street leases – one for 75 years on the ground and terracing to the west, the other for 33 years for the stand and parking area to the east and both dating from 1982 - was one of the last big deals done by the former Hereford City Council.
During the late 1990s, with United facing severe financial problems, the leases were reassigned to property developers in return for a £1m capital injection into the club.
The money was made available through two companies, the BS (Bristol Stadium) Group and Chelverton.
BS and Chelverton took equal ownership of a special purpose company called Formsole Ltd which made the investment and held the leases – as the tenant under both – with the club holding sub-leases.
By August 2001, BS had sold its “loan” to Chelverton which ran into trouble little over a year later when control of the leases passed to Carillion Richardson.
United still owed £1m plus interest to Formsole which stayed solvent when Chelverton went into liquidation.
The reassignment of the leases was supported by Herefordshire Council when it took control of the former city council’s affairs.
Getting the leases back was pitched as a political priority when the news broke in April 2010 that then United chairman Graham Turner and vice chairman Joan Fennessy were ready to sell their majority shareholding in the club.
The club began negotiations with Carillion Richardson for the return of the leases almost as soon as the Keyte-Russon takeover was completed in June that year.
That deal was done by December with the club paying £452,000 to secure the return of the leases and settle a £1,069,500 debt to Richardsons Developments, clearing the way for a new single lease and the development opportunities that could bring.
The deal was intended to offer the club security for the next 30 years and ensure future re-entry to the Football League - which requires a 25-year secured tenancy.
It also opened up opportunities for grant funding for any future development - £400,000 in the Conference and £750,000 in the Football League.
The council was ready to allow an extension to the new stadium lease of 250 years once development at either end was underway, with proceeds from the sale of development areas held in a joint escrow account.
That money was intended for the construction of two new stands - one at each end of the ground - and modernisation work on the existing stadium.