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.
Source: BBC Sport
Source: BBC Sport