Mr Haigh has been accused of fraud by the Dubai-based group and is currently in custody while authorities decide whether to pursue a criminal case.
Speaking from his cell, he told the BBC he would reveal "damaging allegations" about the group's financial conduct.
GFH Capital said it could not comment on "general accusations".
Mr Haigh, 36, was employed by GFH when it purchased Leeds United in December 2012 but resigned as an employee following the club's takeover in April.
Speaking exclusively from the Dubai police cell, he claimed one allegation about GFH concerned the run-up to the purchase of Leeds United from Ken Bates for more than Â£17m in December 2012.
A GFH Capital spokesman said: "GFH cannot and will not comment on such general allegations, and is concerned about Mr Haigh's protestations of being unable to engage with the claim against him while apparently being able to brief the media at will."
The allegations were contained in a dossier compiled by Mr Haigh "about GFH's professional conduct and practices", according to a statement released on his behalf by UK-based spokesman Ian Monk.
"David shared its full contents with two senior figures at GFH in Bahrain who are thus aware of what it contains," Mr Monk added.
Mr Haigh is accused of profiting from falsified invoices worth about Â£3m while at GFH Capital and prosecutors are investigating whether to press criminal charges.
Mr Haigh returned to Dubai last month believing he was about to discuss a job offer with his former employer - only to be handed over to the police. He has now been detained, without charge, for more than a month.
Dubai law states that if someone is suspected of cheating, a breach of trust or fraud they can be detained for as long as necessary, based on the complexities of the investigation.
In his interview with the BBC, Mr Haigh was softly spoken but appeared extremely anxious.
He said he felt "trapped", not by the UAE's legal system - with which he has no complaints - but by the lack of resources in the cell.
The former managing director is one of about 40 detainees, all of whom are denied access to pens and have to share a single payphone.
Mr Haigh said he was allowed very little time with his legal team in order to mount a defence and was particularly exasperated about his bail of about Â£3.5m - an amount he said he did not have.
GFH Capital said it had no control over the criminal investigation being carried out by the Dubai authorities.
Mr Haigh told the BBC he underwent stomach surgery in the UK before flying to Dubai and remains in lots of pain and unable to eat solid foods.
One of his teeth is also causing him pain and he says he has to take medication to sleep.
He continues to deny all of the charges but told the BBC he regretted "signing blank cheques" and allowing others to act on his behalf, prompted by his hectic travel schedule while working at GFH Capital.
GFH Capital has previously categorically denied that it, or its lawyers, have behaved in any way inappropriately.
The private equity company said it had absolute confidence in the legal systems of both Dubai and the UK, which are investigating the civil and criminal claims against Mr Haigh.
A war of words has erupted between ex-Leeds United managing director David Haigh and his former employer, private equity group GFH Capital.