The offer trumps the £300m bid from Boston Red Sox owner New England Sports Ventures (NESV), already accepted by the club’s chairman Martin Broughton.
Lim is also said to be offering £40m to buy players.
His offer comes on the first day of a hearing at London’s High Court to settle a dispute over NESV’s takeover bid.
Tom Hicks and George Gillett have attempted to scupper the deal, arguing that £300m undervalues the club.
The duo tried to block the deal last week by sacking two board members, managing director Christian Purslow and commercial director Ian Ayre, in a last minute attempt to keep control of the club last week.
Royal Bank of Scotland, which would receive £200m from NESV to clear the club’s debt, is trying to prevent the duo from blocking the deal.
For RBS, Philip Snowdon QC, told the court that Hicks and Gillett were in “breach of contract”.
Lim owns several Manchester United-themed bars in Asia, not a fact that is likely to endear him to Liverpool fans.
He says 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.