Lloyds Banking Group is considering having its registered office in London rather than Edinburgh should Scots vote for independence, banking industry sources have told Reuters.
Lloyds, which owns Bank of Scotland, has finalised contingency planning ahead of the September 18 vote.
The chances of secession have increased with support for Scottish independence rising dramatically in August.
Banking industry sources said Lloyds executives are considering having the group's registered office in London, with Bank of Scotland operating from Edinburgh as a foreign division of the business.
Most of Lloyds' senior executives are based at the company's headquarters in London but the bank's registered office, its official legal address, is in Edinburgh, meaning it would be classed as a Scottish bank in the event of independence.
Lloyds has warned that Scottish independence would impact its cost of funding, taxes and compliance costs.
Scottish-based banks have assets worth 12-and-a-half times the country's economic output and economists have questioned whether an independent Scotland would be big enough to host Lloyds and rival Royal Bank of Scotland.
If Lloyds were to stay in Scotland after it becomes independent, London lawmakers have warned that the Bank of England would no longer be the so-called lender of last resort, to provide a backstop were Lloyds to run into trouble.
Lloyds required a £20.5 billion bailout during the 2008 financial crisis, which left the British government with a 40% stake.
The bank, which is now 25% government-owned, has stressed that it will not make any decisions until after the result is known.
It has said that in the event of a vote for independence it will work with relevant authorities to ensure it can serve customers across the UK.
"The scale of potential change is currently unclear, but we have contingency plans in place," Lloyds told Reuters.
"In the event of a 'yes' vote in the referendum, 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 actions that we believe necessary," Lloyds said.
Scotland's First Minister Alex Salmond has said the country would officially become independent in March 2016 in the event of a 'yes' vote, giving Lloyds and Royal Bank of Scotland 18 months to assess their options.
During the intervening period, politicians on both sides of the border would negotiate key questions including whether Scotland can keep the pound.
The three main UK parties have ruled out a currency union but Salmond has insisted they would negotiate if Scots vote for independence and has said no one could stop Scotland using the pound informally.
Some banking industry and political sources say the 18 month timeframe for independence could prove overly optimistic, meaning Lloyds and RBS could have more time to respond.
The sources said Lloyds and RBS have held discussions with the Bank of England over what might happen in the immediate aftermath of a 'yes' vote.
Some executives want the Bank of England to reiterate that it will continue to act as lender of last resort during the transition period and calm any fears among investors and depositors.