The former prime minister said he was ready "any time" to put his case forward and attacked the SNP's arguments for separation.
It came as an ex-SNP and Scottish Government figure said a referendum is “unlikely” to happen within Nicola Sturgeon’s preferred time frame.
Kevin Pringle also warned that, if a vote on leaving the UK is held before the end of 2023, the SNP’s goal of increasing support for independence may be “undermined”.
The SNP wants a second referendum to take place before the end of next year, but the UK Government is unlikely to agree to this.
Mr Brown told The Sunday Times: “I’ve got no doubt we can win a referendum if there is one, and I’m not afraid of a referendum and don’t spend my time thinking about how we can avoid one.
"But there’s no doubt that’s what the government thinks — that they can’t afford to have a referendum.
"I’m not afraid of fighting a referendum or arguing the case in a referendum. I’m ready any time to put my arguments.”
On the SNP's case for independence, he said: “It’s almost like if you say something long enough and passionately enough, enough people will believe it, even if it’s not the truth.
“If Scotland became independent, we’d lose about £10 billion to £12 billion a year in the Barnett formula and also, you’d lose the benefit of the UK welfare state, so you’re talking about a very big gap that’s got to be filled.
"But I’ve got no doubt they’ll produce a prospectus where they will try to argue that there’s no fiscal deficit, even although I think it’s roughly 25 per cent at the moment.”
Mr Pringle, who worked as a special adviser to Alex Salmond when he was first minister and also worked for the SNP and the Yes Scotland campaign, said it is “unlikely” there will be a fresh vote on the issue by the end of next year “given the hurdles to be overcome”.
Writing in The Sunday Times, he said: “I don’t think the war in Ukraine has changed this, in the sense that it was no more likely before the Russian invasion and all the destruction and instability being wreaked.”
He added: “A referendum is a means to an end, nothing more. If the Scottish Government pursues it within a tight 2023 timescale that people are uncomfortable with, even assuming it doesn’t happen then, the task of building support for independence itself may be undermined.”
Mr Pringle said the “mandate” SNP and Green MSPs – who also support holding a second referendum – were elected on in last May’s Holyrood elections was to hold a referendum in the current five-year Scottish Parliament term.
With four years still to go, he added: “That provides time enough to get it right.”
Elsewhere, Ian Blackford, the SNP's Westminster leader, said the war in Ukraine would not affect the party's push for a second referendum.
Appearing on the BBC's Sunday Show, he said: "Is anybody suggesting that Putin should determine the timeline for an independence referendum in Scotland?"