British media reported the owners of the Boston Red Sox baseball team had lodged a bid while the other offer came from Asia. The Red Sox were not immediately available for comment.
"A Board meeting was called today to review these bids and approve a sale," the club said in a statement on their official website on Tuesday.
"Shortly prior to the meeting, the owners - Tom Hicks and George Gillett - sought to remove managing director Christian Purslow and commercial director Ian Ayre from the Board, seeking to replace them with Mack Hicks and Lori Kay McCutcheon.
"This matter is now subject to legal review and a further announcement will be made in due course," the statement added.
"(Chairman) Martin Broughton, Christian Purslow and Ian Ayre continue to explore every possible route to achieving a sale of the club at the earliest opportunity."
A statement from Hicks and Gillett said the offers "dramatically undervalue the Club" but they were committed to finding a buyer that would sustain the future of Liverpool.
"We will however resist any attempt to sell the Club without due process or agreement by the owners," the BBC quoted the American owners as saying.
TERRIBLE START
Hicks and Gillett, who bought the Merseyside club in February 2007 for 218.9 million pounds, instructed Barclays Capital in April to find a buyer and appointed British Airways chairman Broughton to oversee the sale.
The five-times European champions owe 237 million pounds to their major creditors Royal Bank of Scotland, which has set a deadline of October 15 for the debt to be refinanced.
Liverpool, English champions 18 times, have made their worst start to a season in more than half a century with the burden of servicing the debt, leaving new manager Roy Hodgson with little money available to buy new players and strengthen the squad.
Some 7,000 fans marched to Anfield on Sunday before the match against promoted Blackpool waving banners and chanting in the latest protest against Hicks and Gillett.
Liverpool lost the match 2-1 and have now picked up just six points from their first seven league games to sit 18th in the 20-team standings. They have also suffered an embarrassing League Cup defeat by League Two Northampton Town.
The last time they made such a poor start was in 1953/54, when they were relegated to the second division.
