Royal Bank of Scotland has confirmed it has made contingency plans to move its headquarters from Scotland to London if there is a Yes vote in the referendum.
A Treasury source told the BBC that it had discussed the plans with RBS.
Lloyds Banking Group also said it could shift some of its business from Scotland, after customers contacted it for clarification on their finances.
However, the banking group said it was just a legal procedure and “there would be no immediate changes or issues”.
Angus Grossart, chairman of merchant bank Noble Grossart, said that people should “not panic” following the decisions made by the two banks. He told the Financial Times that the impact of a Yes vote was “severely overstated”.
The statement from Lloyds said: “Lloyds Banking Group has seen an increased level of enquiries from our customers, colleagues and other stakeholders about our plans post the Scottish referendum.
“While the scale of potential change is currently unclear, we have contingency plans in place which include the establishment of new legal entities in England. This is a legal procedure and there would be no immediate changes or issues which could affect our business or our customers.
“There will be a period between the referendum and the implementation of separation, should a Yes vote be successful, that we believe is sufficient to take any necessary action.”
Lloyds, in which the UK government has a 25% stake, owns Bank of Scotland and Halifax.
The move of what Lloyds describes as “legal entities” indicates that the banking group is not suggesting there will be a mass relocation of its 16,000 Scottish-based staff. The move would simply mean that the bank would remain protected and regulated by the Bank of England.
RBS, which employs 11,500 people in Scotland, has not yet issued a statement – although there are widespread reports that the bank will clarify the details later in the day.
On Wednesday, insurance giant and pensions giant Standard Life said it was “planning for new regulated companies in England to which we could transfer parts of our business if there was a need to do so”.
BBC economics editor Robert Peston said that that if RBS, 81%-owned by the UK government, moved its head office and registered office to London it “would involve some jobs moving south”.
However, he said the situation with Lloyds was different: “Lloyds would move its legal home to its head office, which is already in London – and that’s unlikely to have much impact on Scottish employment.”
Treasury Chief Secretary Danny Alexander told BBC2’s Newsnight: “When a company like Standard Life says that it would, unfortunately, sadly, have to relocate its business to London that is not some sort of decision that they make lightly.
“They make it on the basis that they regard that as the best way to protect their customers under the new circumstances.
“When we hear Lloyds and other banks making clear that they would have to do the same, again that is not something that they say lightly. They say it having thought about it, having talked to their board and to the senior people in those companies.”
First Minister Alex Salmond has described reports of banks moving out of Scotland as “nonsense” and “scaremongering”.
And Mr Grossart, one of the most senior figures in Scotland’s financial establishment, said people were “overreacting” to the threats of exodus of firms.
“I think it is getting out of hand,” he told the Financial Times. “To hear some of the comments you almost expect people to be predicting a plague of locusts or mice next.”