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Farnell subsequently appealed against the decision and the ban was withdrawn, although he did serve a five-week disqualification period which ended on 14 September.
He is now free to pursue his bid with El Kashashy, which it is believed will be about £200m.
Farnell was previously involved in talks over the future of Bury and was briefly a director at Wigan.
Burnley are regarded as one of the best-run clubs in the Premier League but chairman Mike Garlick’s refusal to loosen the purse strings has led to a strained relationship with manager Sean Dyche, who has repeatedly called for his squad to be strengthened.
His only signing this summer was Brighton midfielder Dale Stephens, while Joe Hart, Aaron Lennon and Jeff Hendrick were all released when their contracts expired in June.
Burnley are currently third bottom of the Premier League, with one point from their opening five games.