Mr Salmond held private talks with Sir Mervyn during his time heading up the Bank of England.
After the last meeting, in June last year, the Scottish Government refused to reveal if the discussions had touched on its plans for a currency union with the rest of the UK in the event of independence.
UK Government ministers, including Chancellor George Osborne, have previously cast doubt on whether this is achievable, stating it is unlikely the UK Government would back such a move.
But Mr Salmond said today that Sir Mervyn had suggested the Treasury could change its approach in the event of a Yes vote.
The First Minister spoke out ahead of a meeting with the new governor of the Bank of England Mark Carney in Edinburgh tomorrow.
He said: "I'm seeing the governor of the Bank of England tomorrow in Edinburgh.
"When I met his predecessor a couple of years back, Mervyn King, the first thing he said to me was 'your problem is what they say now', meaning the Treasury, 'and what they say the day after a Yes vote in the referendum are two entirely different things'."
A spokeswoman for the First Minister said that Scottish Government officials had already had "technical discussions" with their counterparts at the Bank of England, and that these had assisted the Fiscal Commission Mr Salmond set up with its work, including a report proposing a "shared sterling area".
She added: "The First Minister met with the previous governor of the bank, Sir Mervyn King, before and after those technical discussions - and he looks forward to meeting the new governor tomorrow."
Mr Salmond spoke about his meeting with Sir Mervyn during the first public question-and-answer session on the Scottish Government's white paper on independence.
During the meeting in Bathgate, West Lothian, the First Minster predicted turnout in the referendum would be "one of the highest" of any vote in Scotland.
He said: "I don't sense a low vote in this. Everything that's happening just now tells me this is going to be one of the highest polls ever of any election or referendum.
"My evidence for that is public meetings - anywhere you go for a public meeting on this campaign - there's hundreds of people turning up, and that's not normal."
He added that "more people are concentrating more on this decision than any other political decision that I know of in my political career".
Mr Salmond told the audience of about 150 people that the vision his Government had for an independent Scotland was "incomparably better" to anything put forward by the pro-Union parties.
He stressed that the referendum on September 18 gave people "a choice between two futures", adding that the Scottish Parliament had demonstrated that in those areas where it has power "it runs Scotland better".
He said: "The vision of an independent Scotland where we take decisions for ourselves where we mobilise the resources of this country could bring about a better society.
"A vision which is incomparably better than anything from the Tories or Labour, who are mired in negativity.
"That is the positive argument at the heart of the case for independence."
Mr Salmond argued that the current devolved system - where decisions in some areas are made at Holyrood but others are left to Westminster - had "limitations" claiming that "far too often this Scottish Parliament has had to mitigate things that are happening as a result of Westminster policies".
He said: "Independence will give us the opportunity to do better.
"It will give us the powers we need to truly transform this country, to tackle low pay, to halt the growth in inequality.
"We could adopt a new approach to economic growth, with unions and businesses working together, as they do in other European countries.
"We could harness our vast energy resources. We could create a comprehensive childcare system to unleash the potential of all our people."
During a wide-ranging question-and-answer session, Mr Salmond and members of his ministerial team were pressed on issues including teaching reforms, the future of Scotland's voluntary sector after independence and the docking of dogs tails.
The First Minister said the voluntary sector had been under "great pressure because of the recession" but added for the future there should be a "productive relationship where the third sector is seen and valued" for its work, and also for the economic contribution it makes to Scotland.
Mr Salmond added the sector would have a "more important role" under independence, working together with the government to "make things better for people".
On tail docking, Rural Affairs Secretary Richard Lochhead said the issue would be on the agenda in the near future, with a new report to be published on the impact of the ban.
Tail docking has been outlawed in Scotland, with no exemptions made for working dogs.
Mr Lochhead said specific Scottish research had been carried out and added this was "days, perhaps weeks" away from being published.
He said it would then be up to the Scottish Parliament and the Government to look at this, to consider whether some working breeds should be exempt form the docking ban".
On the Curriculum for Education teaching reforms, Education Secretary Mike Russell said Scotland had "hopefully one of the best supported teaching workforces in the world" as he stressed the programme was being rolled out right across the country
Mr Russell said: "In those circumstances we've got a lucky generation of pupils that are coming forward, but we've also got a generation of teachers who we value and support, and if more support is required we will give it."
A Better Together spokesman said later it was a "remarkable coincidence" that Sir Mervyn's reported remarks backed up the Scottish Government's stance.
The spokesman for the pro-UK campaign group said: "What a remarkable coincidence. Just hours before the visit of the current governor of the Bank of England, Alex Salmond makes a claim about something that may or may not have been said by Mark Carney's predecessor. In a double coincidence, this alleged conversation backs up Alex Salmond's arguments.
"The First Minister operates on the basis that people are daft and can't see through his bluster.
"Unfortunately for him, people know when someone is at it. They will be able to see this latest frippery from the First Minister for what it is."