Haigh, 36, has been accused by the club’s former owner Gulf Finance House of wrongdoing under its ownership and in connection with the sale of Leeds to Italian Massimo Cellino.
Haigh, an employee of GFH before he resigned from the Dubai-based equity firm earlier this year, has denied all allegations.
He has been held in custody since arriving in Dubai on Sunday to discuss a possible new job with GFH, it is understood.
A close friend of Haigh’s told the BBC: “David has done absolutely nothing wrong or illegal. He is appalled to find himself in this position.
“However, as someone who knows Dubai well and respects its institutions he is confident that the authorities will see these allegations for what they really are and clear him from any wrongdoing.”
A Foreign Office spokesman said: “We are aware of the arrest of a British National in Dubai on 18 May 2014. We are providing consular assistance.”
Haigh was a key figure in GFH subsidiary firm Gulf Finance House Capital’s purchase of Leeds from former owner Ken Bates in December 2012.
He was appointed managing director of the club in July 2013 and quit his job at GFH Capital in February this year.
In January this year a consortium he was involved with, Sport Capital, failed in its bid to buy Leeds, but he also played a key role in paving the way for Cellino to complete his takeover in April.
Sport Capital served a winding-up order on Leeds last month over a B£950,000 loan. The club and Cellino are contesting the petition and the case will be heard by a judge in London on June 9.
Haigh was due to be made chief executive of Leeds under Cellino’s ownership, but resigned shortly after the takeover was completed following comments made by the Italian, who also stated publically he was going to sack him.
Haigh attended a voluntary interview with West Yorkshire Police earlier this month as part of its investigation into the installation of surveillance equipment at Elland Road.
He admitted to overseeing the installation of cameras in the club’s boardroom, which became a police matter following allegations that it may have been funded as a result of a misappropriation of club funds.
A statement released by Haigh’s solicitors, Olliers, at the time said: “As the former managing director of the club, David was fully aware of the installation of these devices which were quite properly paid for by the club.
“They were put in place following reports which he received between the end of January and early March this year alleging the recent misuse of Class A drugs in and around the boardroom. One of these reports was made by police.”