Leeds "is one of the best supported clubs in English Football with a higher than average match day attendance than most Premier League teams," Gulf Finance House said on Thursday.
Last week, Leeds chairman and its controlling shareholder Ken Bates, said talks on a potential investment in the club, which last won the English title in 1992, were at an "advanced stage".
Citing a confidentiality provision, GFH gave no financial details or any indication of when an acquisition might take place. Company officials were not available to comment on whether the Bahraini unit would provide all the money for the purchase or whether other investors might be involved.
GFH added the club would benefit financially from a recent renegotiation of television broadcast rights if it won promotion to the Premier League.
The club has had a turbulent past decade, both on and off the pitch. Having reached the semi-finals of the UEFA Champions League in 2001, the club was relegated from the Premier League in 2004 and dropped into League One in 2007. It gained promotion back to the Championship in 2010.
The on-field descent came against a backdrop of financial woes, which forced the club to sell key players and ultimately led to administration in 2007.
"If you look back since the start of the Premier League, Leeds are without doubt the most successful club not to be in it right now," said Dan Jones, partner at Deloitte's Sports Business Group.
"If you can return it to the Premier League, then it could return to being one of the top 20 clubs in the world by revenue - that's the scale of the club you're dealing with."
Bates said both parties were working towards concluding the deal "as soon as possible", according to a statement on the club's website.
Bates is a familiar figure who was the previous owner of Chelsea for more than two decades before selling to Russian oligarch Roman Abramovich in 2003.
The acting CEO of GFH, Hisham Alrayes, and representatives of GFH Capital attended Saturday's game between Leeds United and Nottingham Forest, according to press reports.
An acquisition would add to a string of investments in European teams by Middle Eastern interests over the last several years.
Manchester City, the current English Premier League champions, were bought by a member of the Abu Dhabi royal family in 2008, while Kuwait's al-Hasawi family bought twice European Cup winners Nottingham Forest in July this year. France's Paris St Germain and Spain's Malaga are owned by Qatari investors.
However, not all football clubs have benefited from Middle Eastern backing. Spain's Malaga were forced to sell some of their best players in the summer due to funding issues, while Portsmouth have been forced into administration twice in the last three years.