He did not identify any locations but a Sunday Telegraph report suggested the possibilities included Singapore or Brunei in the South China Sea and Montserrat or Guyana in the Caribbean.
The defence secretary also downplayed the significance of his announcement that 3.500 troops were being put on standby, describing it as “good sensible planning to make sure that everything runs as smoothly as possible”.
In an interview with the Sunday Telegraph, Mr Williamson said that Britons should be “much more optimistic about our future as we exit the European Union”.
He said: “This is our biggest moment as a nation since the end of the Second World War, when we can recast ourselves in a different way, we can actually play the role on the world stage that the world expects us to play.
“For so long – literally for decades – so much of our national view point has actually been coloured by a discussion about the European Union.
“This is our moment to be that true global player once more – and I think the armed forces play a really important role as part of that.”
Mr Williamson said that Brexit would allow the UK to change the 1960s policy of withdrawal from regions “east of Suez”.
“I am very much looking at how can we get as much of our resources forward based, actually creating a deterrent but also taking a British presence,” he said.
“We are looking at those opportunities not just in the Far East but also in the Caribbean as well.”
The defence secretary also claimed that recent research showed the British underestimated the potential for UK global influence.
He said that while “the rest of the world saw Britain standing 10 feet tall – when actually we stood six feet tall – Britons saw us standing five feet tall, not the six, and certainly not the 10.”
Mr Williamson also predicted Australia, Canada, New Zealand, Caribbean states and nations across Africa would look to the UK for “the moral leadership, the military leadership and the global leadership”.
Additional reporting by Press Association
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