A Scottish-led consortium was interested in a merger with the troubled Dunfermline Building Society, BBC Scotland has learned.
The Dunfermline was taken over by the Nationwide on Monday after the UK Government announced Scotland's largest society was to be put on the market.
A statement from Scottish Friendly Assurance said a consortium approached the Dunfermline in the middle of March.
But they were not allowed to speak to the mutual until Sunday.
Stuart Bernau, executive director of Nationwide, told BBC Radio Scotland's Good Morning Scotland on Tuesday he would be "looking to preserve as many jobs as possible".
The Dunfermline, founded in 1869, has 34 branches and a headquarters in Fife, employing 530 people in total.
It is expected the mutual will announce £26m of losses for last year.
The Treasury ruled out a UK Government bailout of up to £100m after regulators said the move was not viable.
A statement from Scottish Friendly Assurance said: "Initial approaches were made in the middle of March to the Dunfermline Building Society, with Scottish Friendly joining the consortium shortly thereafter.
"Although numerous attempts were made to open exploratory negotiations with DBS, we were not given an opportunity to meet with them until Sunday 29 March, less than 24 hours before a deal was announced.
"While we are of course pleased that the position of DBS members has been secured, the announcement of today's deal with the Nationwide precludes a Scottish-led solution that may have been a possibility if talks had been agreed between the consortium and DBS at an earlier stage in the process."
The Dunfermline brand name will live on after the takeover
Dunfermline's board - including chief executive Jim Willens, who is a former board director of Nationwide - will resign after the deal.
Mr Willens said: "I am not in a position to comment on any individual approaches.
"What I can say absolutely 100% is that any proposition or proposal put to the society was looked at thoroughly and immediately."
Outgoing chairman Jim Faulds confirmed to BBC Scotland that he had been unaware of the approach by a Scottish-led consortium until Thursday of last week.
The Nationwide is to buy all the Dunfermline's branches, good loans and deposits, although the brand name will remain.
The Treasury will take on about £1.6bn of commercial property lending and acquired mortgage debt under the deal.
Independent MSP Margo MacDonald said: "I have been given in confidence some record of the exchanges that took place and they were perfectly serious.
"They wanted to explore the possibility.
"No-one is saying that it would definitely have come off, but who knew about that offer being made? Did the chief executive tell everybody?"
The SNP's Treasury spokesman, Stewart Hosie, demanded answers from the UK Government.
He said: "The possibility of alternative bidders, including a Scottish-based bid that could have seen HQ functions and jobs remain in Scotland, is something that all parties should have been aware of prior to the deal with Nationwide.
"Revelations of a possible bid from a Scottish-led consortium and the speed at which decisions appear to have been made only add to the catalogue of questions that the Treasury and the FSA must answer.
"There is a certain feeling of deja vu over the Dunfermline deal in the sense that, just like HBOS, this is another Scottish institution which appears to have been sold off in haste without a thorough examination of the options."
Mr Bernau said Nationwide had initially been approached a few weeks ago to "see whether it was possible for us or other people to take over or merge with the Dunfermline".
But he added that, after some work was done, the society "couldn't see how taking it over would actually work for us".
He said: "What actually happened is, on Friday evening at about eight o'clock, the Treasury and the Bank of England and the FSA decided that they couldn't find a solution of someone to take it over or invest capital, so they decided that the best way to do it was to invite organisations to bid for the various assets and liabilities.
"We were involved the whole of the weekend, through the night on Saturday and Sunday, and it was confirmed at 0745 BST on Monday that our bids had been successful to take over the prime mortgage book and to take over the savings."
Mr Bernau added that was because the Nationwide would "guarantee the branches and because we would continue to run it as a regional brand".