Burnley are the subject of a £200m takeover bid from Egyptian businessman Mohamed El Kashashy and lawyer Chris Farnell.
It had been thought American sports investment firm ALK Capital were in pole position to buy the Clarets.
However, BBC Sport understands that Farnell and El Kashashy are in talks with major shareholders at the club.
Farnell recently had a ban from owning a club in England overturned by the Football League.
The Cheshire-based lawyer was handed a ban after issues arose during an attempt to buy Charlton earlier this year.
Farnell subsequently appealed against the decision and the ban was withdrawn, although he did serve a a five-week disqualification period which ended on 14 September.