Gordon Brown said such a move was a "possibility" but not in the short-term.
His comments come days after similar statements from Scottish Labour leader Iain Gray and Scots Secretary Jim Murphy.
His speech to the Labour Party conference included the pledge of a referendum on changing the Westminster voting system.
Mr Brown denied the speech had little to offer Scotland.
He also highlighted last year`s banking rescue as an argument for Scotland remaining part of the Union.
And defending Labour's current opposition to a Scottish constitutional referendum, he said Iain Gray was "absolutely right" to argue it was wrong to stage this during a recession.
Mr Brown said: "You can debate these things for the future but the important thing at the moment is I don`t really think people want me to be obsessed with the constitutional issue this month or next month.
"I think what they want us to do is concentrate on making sure the economy comes through recession."
He said the Royal Bank of Scotland and Bank of Scotland had "collapsed" with the biggest debts in the history of British banking, and were rescued by the UK Government.
"There`s no Scottish administration that could have rescued these banks," he said.
"It would have been an Iceland situation because the debts of these banks were many more times the Scottish national income.
"As part of the United Kingdom, at great difficulty, we were able to come in to buy shares in these banks and make sure these banks stayed in business."
Asked if he could see a time when a future Labour Government offered a referendum to settle Scotland`s constitutional future, Mr Brown replied: "Of course that`s a possibility.
"The Calman report recommends new devolution arrangements, and obviously these are big changes that will make devolution work better.
"But they are not separation."
And he said voters at the next election would not want to see "a party of separation" getting votes at the expense of a party that represented Scotland "very fully" as part of the UK.
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