Talks between the Bahrain-based investment bank and United chairman Ken Bates have been ongoing for weeks and the two parties now have additional time to finalise a deal.
David Haigh, deputy chief executive officer at GFH Capital, said in a statement: "The fact that we are in such advanced talks means this extended exclusivity window is merely to ensure we can get past the final post without distraction.
"We have come so far and are looking forward to what we hope will be a positive statement about change in ownership of Leeds United shortly."
In April last year Bates announced he had bought a controlling 72.85 per cent stake of the club's shares from a Geneva-based company, Forward Sports Fund, while the club have made pre-tax profits of more than £10 million since the summer of 2007.
Leeds fans were perplexed by the further extension after the club disclosed as far back as May that it was in talks with potential investors.
"This (announcement) doesn't make any sense. Why didn't they put a fit and proper person request months ago? The Football League says that is the only test a new owner would have to pass," said Gary Cooper, chairman of the Leeds United Supporters Trust.
"The supporters deserve much better than this," he added. The Trust represents around 8,000 fans and has clashed with Bates in the past.
Foreign investors are increasingly looking at larger Championship clubs, hopeful of them winning a place in the big money Premier League.
Leeds have won the English league title three times, most recently in 1992. However, the current team is without a win in six league games and have slipped to 18th place in the 24-team Championship.
Fans hope that new owners will be in place in time to fund signings in the January transfer window to allow the team to make a late push for a promotion place.