The Binnies, founders of investment company Carlisle Capital, have submitted a bid of about £28m.
The club's administrators had hoped to name a preferred bidder earlier this month, with three parties interested.
But they have to meet the English Football League's statutory requirement for proof of how Derby will be funded for the rest of the season.
BBC Radio Derby reports that the bid does not cover the Rams' Pride Park stadium, which is owned by former club chairman Mel Morris.
Derby were placed into administration last September by Morris and the club were hit with deductions totalling 21 points, leaving them facing relegation to League One.
Despite that, impressive form under manager Wayne Rooney has seen the team climb off the bottom of the table and they are within eight points of safety.
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!