Liverpool have been given a ten-day deadline to accept Kenny Huang's offer to buy the club's debt.
The Sun says if they have not given an answer by then, the Chinese billionaire will walk away.
Huang, head of Hong Kong-based investment company QSL Sports Ltd, wants to take over the £237million RBS loan handed to the unpopular American owners Tom Hicks and George Gillett.
Liverpool themselves are treating him as a serious bidder and chairman Martin Broughton - the BA supremo brought in to sell the club - has opened talks with Huang's group.
Huang is adamant he will make hefty funds available to bring in world-class players and tempt stars such as Fernando Torres into staying at Anfield.
But he has insisted on an answer from Liverpool by the end of next week - or he will pull the plug.