Kezia Dugdale said she believes Mr Corbyn would agree to a referendum if it meant getting the keys to Downing Street, but that he would likely “make a Socialist case for the United Kingdom” in any campaign.
Ms Dugdale, who will finish her career as a Lothians MSP next month to take up a new role, also predicted Boris Johnson could “gamble” by holding an independence referendum if he becomes prime minister.
Speaking in a BBC interview yesterday as the Scottish Parliament broke for summer recess, she said she believed a second independence referendum was increasingly likely, but that people would still vote against independence because of the “nuts and bolts” of the economy.
Ms Dugdale said: “Boris Johnson, being a gambler, might roll the dice on indyref2 because he feels like it. That’s how flippant he can be.
“But the flipside is that in a general election where Jeremy Corbyn comes within a fag paper of wining a majority, but has to look to other parties for support, I can see a scenario where the SNP goes to Jeremy Corbyn and says ‘we’ll vote for every one of your budgets in the lifetime of your Parliament in return for indyref2’.
“And at that point Labour has to decide ‘does it appease the SNP and give them indyref2 to be in power or does it give up the prospect of being in power to protect the Union?’
“I think he would probably appease the SNP – not because I have any inside track on that, but when I look at how he and John McDonnell talk about that prospect they’re never 100 per cent definitive.”
She added: “That’s why I think indyref2, but not independence, is more likely. I think it’s a serious prospect and I don’t say that in any attempt to cause a political drama, though I’m sure some people will see it that way.
“But in that moment, at that point, where he has fought to be a Labour Prime Minister and his whole life has been about living out his socialist dream as Prime Minister, and it hangs in the balance with the granting of a referendum – not independence, but a referendum – in which he can make a socialist case for the United Kingdom, it’s hard to see why he would walk away from power at that moment. It’s just my feeling.”
Ms Dugdale has previously expressed her frustration with Mr Corbyn’s stance on the constitution during her two years as leader of Scottish Labour. Even last September he said he was not “ruling out” a second vote, and would decide on the issue “at the time”.
Ms Dugdale also ruled out any “project fear” tactics of a future No campaign.
“If we learned anything about the debate on independence in 2014 it was that it’s all about the economics, how people feel financially and the economic security of their families,” she said.
“But in indyref2 some of the scenarios that worked then won’t work now – those project fear scare stories of not being able to buy milk the next day. But when you boil down to the rational nuts and bolts about what currency you would use or who your lender of last resort would be, that’s not project fear, but serious questions and the answers are not there.”
A Labour Party source last night downplayed the prospect of Mr Corbyn agreeing to another referendum.
The source said: “There’s not a shred of evidence for this. Jeremy has made it clear time and time again that he thinks independence is a bad idea and would be economically disastrous. We will not be cutting deals with the SNP or anyone.”
First Minister Nicola Sturgeon has said she wants to hold a second independence referendum within the next two years and the Tory leadership battle has seen many of the contenders rule out the prospect.
However, a recent poll of Conservative members suggested they were happy to sacrifice the UK as long as Brexit was completed. Tory leadership frontrunner Boris Johnson also came under pressure yesterday from Scottish Conservative leader Ruth Davidson on the issue of his support for the Union.
She said: “I want to see him [Boris] make assurances that it’s not Brexit do or die, it’s the Union do or die. That’s exactly what we’ve seen from the other candidate in the race and that’s why he’s going to get my vote.”
Mr Johnson had earlier said he had a “very good relationship” with Ms Davidson, prompting the SNP to say it was the “ultimate embarrassment” for her.
SNP MSP Tom Arthur said: “No matter how hard she tries to distance herself from Boris Johnson, she cannot and will not be able to shake off the fact he is soon likely to be her boss. And if he does become PM, the questions will only start piling up for her when it comes to backing his policies.
“Ruth Davidson has a long track record of flip-flopping and no-one should expect anything else from her if Boris Johnson enters Downing Street.
“Having already backed two losing contenders for the Tory leadership, her endorsement of Jeremy Hunt is unlikely to end well. But the reality is that either Johnson or Hunt would be disastrous prime ministers for Scotland.”
In the same BBC interview, Ms Dugdale said she thought Mr Johnson should answer questions about his personal life and accused him of playing a “tactical game”.She added: “When you’re in a privileged position of leadership, to have the honour of that role, you have to open yourself up to a free and democratic press.”
And she believes a general election in October, before the Brexit deadline of Halloween, is increasingly likely.
She said: “Boris is a gambler, and I think he’ll say I’ll have a General Election sure - if it’s between me who they can trust to take us out [of the EU] or him who’ll keep us in.”