Mascherano was at the club's training ground on Tuesday after manager Roy Hodgson insisted the midfielder will only leave if the club's valuation is met.
The club's parent company is ₤350million in debt, and up for sale, but it is understood Liverpool's main creditor, Royal Bank of Scotland, is putting no pressure on Hodgson and the board to accept any offer.
"There's absolutely no pressure from the banks to sell players," a club source told Sky Sports News HD.
"The debt is with the owners. The club runs itself. RBS aren't interested in asset-stripping Liverpool."
RBS's main ₤237million loan to the club expires on 6th October and must either be repaid or, if a new agreement can be reached, rolled over. But the bank could take control of the club's shares.
"₤16m from the sale of a player, such as Mascherano, is hardly going to make much of a difference to a club with a debt of ₤350m." added the source.
"RBS appears to have faith in Martin Broughton, and Barclays Capital, in their search for a new buyer."