Lord King said he did not see “any major problems” over the question of which currency an independent Scotland would use.
But he said it could, however, be a challenge to borrow money on the international market.
The Scottish Government wants a referendum on independence to take place between autumn 2018 and the spring of the following year in the wake of the Brexit vote.
But Prime Minister Theresa May has said “now is not the time” for another vote and has indicated that her government would reject the SNP’s preferred timetable.
Lord King, who was at the helm of the Bank of England until 2013, made the comments during an interview on BBC Two’s Newsnight programme.
He said: “Scotland certainly could be an independent country. There are plenty of small countries the same size as Scotland.
“Scotland has both the people, it has the capital city, the history, the culture. It could be an independent country. The question is, does it want to be, given the consequences of it?”
The issue of the currency that would be used by an independent Scotland proved to be a key economic battleground during the campaign surrounding the 2014 independence referendum.
The SNP argued that Scotland should share the pound with the rest of the UK.
When the policy was put forward in the run-up to the vote, it was rejected by then chancellor George Osborne and other leading Westminster politicians - and was seen as one reason why the Yes campaign failed.
Lord King told Newsnight: “I, myself, don’t think there are any major problems in terms of currency - that was the thing that project fear focused on last time.
“But there is an issue about public finances.
“And if the oil price remains low and if they lose the money which is transferred from the rest of the United Kingdom to Scotland, then they would have to make that up in their own budget, but that’s a consequence of deciding to be financially independent, you end up paying for yourself.
“And it would be a challenge, I think, to borrow on the international market if Scotland decided to run a large budget deficit.
“I think that would be expensive, the interest rate would go up. But that’s one of the consequences of saying ‘if we want to be independent we have to accept the consequences’.”
Responding to the comments, an SNP spokesman said: “Mervyn King is absolutely right in concluding that, of course, Scotland could be an independent country - we have huge economic strengths and solid foundations on which to build.
“We’ve seen so many of the promises made to the people of Scotland in 2014 unravel - not least that if Scotland voted No we would keep our EU membership.”
He added: “We will be frank about the challenges we face to grow our economy but equally serious about the opportunities of independence.
“That is exactly the focus of the SNP’s growth commission, which will set out in the coming months how Scotland can work sensibly and progressively to maintain a sustainable budget position.”