Nicola Sturgeon has repeatedly warned a fresh vote is "highly likely".
But Scottish Labour Kezia Dugdale has said her party would oppose any attempt to hold a referendum.
However, Mr Corbyn told the Press Association it was not the job of Labour "to prevent people holding referenda".
His comments come amid speculation that Ms Sturgeon, the Scottish first minister and SNP leader, is about to demand a Section 30 order from Westminster, allowing another legally binding vote on Scotland's place in the UK to be held.
Prime Minister Theresa May has so far avoided saying whether or not she would grant permission - instead saying only that she does not believe a second referendum should be held.
Mr Corbyn suggested he did not think Westminster should seek to block a referendum, and was quoted by PA as saying that Labour "wouldn't block it".
He added: "If a referendum is held then it is absolutely fine, it should be held. I don't think it's the job of Westminster or the Labour Party to prevent people holding referenda."
He also stressed the importance of the economic ties between Scotland and the rest of the UK, and on the issue of further devolution stressed any new powers transferred north as a result of Brexit should go further than just Holyrood.
Mr Corbyn said: "I do think we should set it within the context of the economic relationship with the rest of the UK and the question of devolution of EU to English regions and to Scotland, and to parts of Scotland rather than just to the government in Holyrood.
"The principle of regionalism is it goes to everybody within a region, not just to the central powers and the SNP have a bit of a tendency to centralise things around themselves."
The Press Association later reported it had been told by a source close to Mr Corbyn that the Labour leader believed that: "Westminster blocking a second referendum would give the SNP exactly what they want - more grievance."
The source added: "Kezia Dugdale is absolutely right to oppose a second referendum at Holyrood and to keep the pressure on Nicola Sturgeon to rule one out.
"However any hypothetical deal on a second referendum is highly premature as there would need to be lengthy negotiations around the timing and the question on the ballot paper, given the remain/leave precedent set in the EU referendum."
Mr Corbyn was speaking ahead of a speech to Labour's economic conference in Glasgow.
Ian Murray, Scotland's only Labour MP, subsequently tweeted that Mr Corbyn was "destroying the party" and that "supporting another indyref goes against wishes of Scots".
Mr Corbyn's comments appeared to echo those of former Liberal Democrat leader Nick Clegg, who told the Herald newspaper that it would be "very difficult for any government of any composition in London to try and impose a fatwa on any move towards a referendum, if that was something which was being pushed, however unwelcome that is."
However, Scottish Lib Dem leader Willie Rennie told ITV Borders that the party would vote against a referendum in both Holyrood and Westminster.
SNP MSP Stuart McMillan said Mr Clegg and Mr Corbyn had "both recognised the Scottish government's cast-iron democratic mandate for a second independence referendum if that is the chosen route to protect our national interests."
He added: "This was a specific manifesto commitment on which the SNP was re-elected just 10 months ago.
"Scotland voted clearly and decisively to remain in the EU: not for an economically disastrous Tory hard Brexit outside the Single Market, and yet Lib Dem and Labour MSPs will happily sit on their hands and let that happen.
"It's embarrassing that Lib Dem and Labour in Holyrood want to deny Scotland the opportunity to avoid a damaging hard Tory Brexit while Corbyn and Clegg agree that it would be wrong to block Scotland having a choice on our future if that is what is needed."
Scottish Conservative chief whip John Lamont said: "Jeremy Corbyn clearly doesn't understand that most people in Scotland don't want another divisive referendum.
"A second referendum on independence should not take take place and, unlike Mr Corbyn, the Scottish Conservatives will not support the SNP in making it any easier to take place.
"The less he says on this issue, the better."
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