Owner Steve Dale has told BBC Radio Manchester he has agreed a deal to sell Bury, as a deadline for their possible expulsion from the EFL approaches.
Bury have been given until 23:59 BST to prove it can pay off creditors and has funding to complete the season.
BBC Radio Manchester has contacted the English Football League for comment.
A statement given to PA Media, Newman and Campbell said: “We can confirm that over the past 10 weeks we have been in discussions with Bury FC, the EFL and others with a view to putting forward a proposal to buy the club.
“It is a very complicated scenario and there remain a number of outstanding legal and other issues that have to be addressed.
“Our background is in football and data analytics and it should therefore not be surprising that we are taking a very detailed forensic look at the realities of Bury FC’s finances.
“A club like Bury ought to have a viable long-term future even if the short-term future is clearly very challenging. To that end we have been in discussions with the EFL about an extension so that we can continue to explore the prospects for a purchase.”
The EFL’s most recent update, issued at 17:00 BST, said “limited progress” had been made in either providing the evidence they required or finding a new owner but it would “keep working to find a resolution”.
Dale told the BBC earlier on Friday that he had found a “prospective buyer” who was “waiting for the EFL to come back to him on a few points”.
He carried out numerous media interviews throughout the day and had earlier asked members of the public to pledge money to help “save a football club”.
‘A massive step forward’
EFL chief executive Debbie Jevans said earlier this week that a short extension to the deadline may be granted if a buyer could be found.
And Bury North MP James Frith, who had earlier claimed a bidder he had been liaising with was going to submit the relevant documentation to the EFL on Friday, said Dale’s announcement was a “massive step forward”.
He told BBC Radio 5 Live: “This is not over the line fully, there are a lot of questions to be answered about the complexity of the financial situation, but it is their (Newman and Campbell) bid that Dale is referencing.
“I don’t think the EFL have any reason now not to extend the deadline.
“It is a time to breathe a sigh of relief, but it’s not 100% due diligence water tight.”
On 9 August, Bury were given 14 days to provide evidence of financial viability to the EFL or risk expulsion from the league.
The Shakers have had their first five league games of the season suspended by the EFL and they were also withdrawn from the Carabao Cup.
No club has been removed from the EFL since Maidstone were liquidated in 1992.