Peter Lim, a Singapore billionaire, is offering £320m in cash for Liverpool football club and its liabilities.
The offer trumps the £300m offered by New England Sports Ventures (NESV) which was accepted last week by Liverpool's chairman, Martin Broughton.
BBC business editor Robert Peston says Mr Lim is also offering to provide £40m in cash to buy players.
He adds Liverpool's board will find it difficult to ignore the offer, raising more uncertainty about the club's fate.
Mr Lim said in a statement: "I respect and admire Liverpool Football Club which is steeped in tradition and history. I am committed to rebuild the club so that it can soon regain its position at the pinnacle of English and European football, where it truly belongs.
"This is why I have stepped forward with this offer," he said.
The offer coincided with the start of a case in London's High Court to resolve a power struggle on Liverpool's board of directors.
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Royal Bank of Scotland, which holds the bulk of Liverpool's debts, is seeking a court order preventing the club's co-owners, Tom Hicks and George Gillett Jr, from removing two board members.
Philip Snowdon QC, for RBS, told the court that Mr Hicks and Mr Gillett were in "breach of contract" and guilty of "breath-taking arrogance".
But Paul Girolami QC, representing the American owners, said his clients "were not trying to throw a spanner in the works" of the proposed sale deal.
He said there had been other offers for the club which potentially were better than the one from NESV.
"What has happened is that the English directors have gone forward with the NESV bid without properly considering alternatives when those alternatives at least appear to give better prospects," Mr Girolami said.
He disclosed in court that there was a bid from American hedge fund Mill Financial to pay off all the club's debt and commit £100m to a new stadium.
Mill Financial helped support a previous refinancing of the loan used by Mr Gillett to buy the club in 2007. The hedge fund now technically controls Mr Gillett's 50% stake.
The High Court judge, Mr Mr Justice Floyd, later confirmed that he make his ruling on the case at 1030 BST on Wednesday.
Mr Lim, whose previous bid for Liverpool was rejected in favour of New England's, has an estimated net worth of $1.6bn (£1bn), according to Forbes magazine.
He made his fortune in fashion, logistics and agri-business.
His interest in English football stems from his ownership of several Manchester United themed bars in Asia - which have persuaded him that there is huge global potential for making money from top-flight English football.
There have been suggestions that he intends to sell the Manchester United bars if he secures control of arch-rival Liverpool.
What may excite Liverpool fans about the offer is that Mr Lim is promising money for new players.
He said in his statement: "The club needs to strengthen its existing squad. As part of this offer, I will be injecting £40m in cash into the club for Roy Hodgson to bring in new players during the upcoming transfer window. Liverpool needs to start winning again.
"I believe that if its massive debt burden can be removed, the club would be able to focus on improving its performance on the pitch.
"My offer pays off the existing owners' bank acquisition debt and also frees the club of its own bank debt," he said.