The UK-based board members are keen to pursue advanced negotiations with one or both parties but American co-owners Tom Hicks and George Gillett have rejected the offers.
An attempt to re-finance the club by Hicks and Gillett is also understood to have been rejected by chairman Martin Broughton and the board.
Both bids are reportedly in the region of £300m - enough to cover the club's debts to RBS and provide a small transfer kitty for Roy Hodgson - but Gillette and Hicks have allegedly rejected the deal on the basis that it does not offer them a return on their investment.
However, and more importantly, both bids have been given the seal of approval by RBS who have given the club until 15th October to repay its loans.