Chinese businessman Kenny Huang is one of "several" potential buyers to submit a bid to Liverpool chairman Martin Broughton, BBC Sport reports. Huang, who is the head of Hong Kong-based investment company QSL Sports Ltd, values the club at about £350m.
But it is understood that as many as six bids were submitted last week.
Broughton and investment bank Barclays Capital, who are leading the sale, will elect a preferred bidder by the end of next week.
While RBS has told the BBC it is not negotiating directly with Huang, it is understood he is mounting a credible bid.
However, he wants the deal to be completed within two weeks to allow Hodgson time to strengthen the squad before the transfer deadline at the end of August. Any later and the deal is off.