Mr Murphy said there was still no detail to the mystery bid
Lloyds TSB is widely expected to present the details of its takeover offer for troubled bank HBOS later.
Shareholders must approve the offer - which has been reduced twice - before the merger can go ahead.
Lloyds TSB has said that if successful, it will cut running costs by £1bn, which has led to fears of widespread job losses at HBOS.
Meanwhile, the Scotsman newspaper has reported that a foreign investor may also be interested in bidding for HBOS.
It is the third potential bidder to be discussed, after Scots entrepreneur Jim Spowart said on Saturday that a European financial services company was interested in making an offer.
Scottish Secretary Jim Murphy insisted later that despite the speculation there was still only one bid - that from Lloyds TSB - on the table.
Since the government first brokered the deal to save HBOS six weeks ago, Lloyds TSB has twice renegotiated the terms of its takeover to reduce the amount of stock it will give HBOS shareholders.
HBOS shareholders will now get 0.605 Lloyds shares for every HBOS share, compared with an earlier offer of 0.833. Initially, there had been proposals for a one-for-one share swap.
While investors may welcome the news of cost savings, HBOS staff are worried.
The BBC's business correspondent Joe Lynam said that to reduce overlap between the two banks there was likely to be "de-duplication" of jobs, especially in the insurance arm.
HBOS has a total of 72,000 staff while Lloyds TSB has more than 74,000 employees worldwide.
The Scotsman reports claims from the SNP's Alex Neil that the latest party to show interest in HBOS is based abroad and does not have a major high-street presence in the UK.
This would be more likely to protect jobs in the UK, as there would be no overlap of employee roles.
The newspaper reported the firm had made preliminary inquiries about an offer, but was not as far through the process as the other potential bidder brought to light by Mr Spowart.
No details about the terms or the identity of the party have been given but the interest is "genuine", according to Mr Spowart.
He said the possible new bid, if successful, would "keep decision making in Scotland".
The government has pumped £17bn into HBOS to prevent it going under, meaning that taxpayers would own about 40% of the merged institutions if the Lloyds deal goes ahead.
Minister have also overruled concerns about competition raised by the Office of Fair Trading in order to allow it to proceed.