Broughton was chairman of the British Horseracing Board for three years
Liverpool are set to appoint a new chairman and ask a new bank to lead their search for fresh investment, BBC Sport understands.
Martin Broughton has been approached, with the British Airways chairman considering forming part of a restructured board at Anfield.
Barclays Capital, the bank's investment arm, will head the latest attempt to find a new buyer for the club.
Co-owners Tom Hicks and George Gillett are ready to step down as co-chairmen.
The Americans believe that by presenting a united front, potential investors are more likely to be found.
Broughton has previously chaired the British Horseracing Board, and is a lifelong Chelsea fan.
He is also a former chairman of British American Tobacco, and the Confederation of British Industry.
Hicks and Gillett were seen together at Anfield for the first time in almost six months for Liverpool's 4-1 win over Benfica in the Europa League quarter-finals on Thursday and have been holding talks over the club's future.
Last week, the American pair rejected a £100m offer for a 40% stake in the club by the Rhone Group, a New-York based private equity firm, to the dismay of manager Rafa Benitez.
Liverpool have been asked by its principal creditor, the Royal Bank of Scotland, to reduce their £237m debt by around £100m, with the current lending arrangement running until this summer, although that could now be postponed.
A further refinancing deal, and the construction of a new stadium, depends on fresh capital being found.
The club's managing director, Christian Purslow, has been trying to find new investors for several months with the help of investment banks Merrill Lynch and Rothschilds.
Meanwhile, manager Rafael Benitez has hinted he needs £60m to bring in new players next season - but he conceded he will have to offload some players to raise funds.
He said: "The cost of a top-class player is about £20m. I think we need three.
"We want to keep the spine of the team. But sometimes you have to manage and you have to sell two or three players who aren't playing many games.
"I think we can improve but it depends if we can do the right signings and it is always easier to sign more players with more money."
Last summer Benitez spent £20m on Alberto Aquilani, who has struggled with injury since arriving at Anfield.
"Sometimes you bring someone who needs to settle down or they have a problem - this year we had a problem with Alberto Aquilani and his ankle - so you cannot guarantee anything," Benitez said.
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