The SNP leader said on the election campaign trail today that Mr Corbyn, as Prime Minister, would grant the transfer of power to Holyrood allowing a repeat of the 2014 vote on leaving the UK. Such a move is widely seen as a concession to the SNP in exchange for Nationalist MPs backing him as Prime Minister in the event of a hung Parliament.
Mr Corbyn said earlier this week a second vote could happen in the "later stages" of a Labour Government.
But in a statement issued tonight, Corbyn said: "Labour does not support independence for Scotland and we do not think another independence referendum is either desirable or necessary.
"We are running the most radical, people-focused election campaign the UK has ever seen and if we win we will invest £70 billion in Scotland over the next decade. Our promise to the people of Scotland, and people across the UK, is that a Labour government will end austerity, tackle the climate emergency and invest in our communities to truly transform society."
Ms Sturgeon ramped up the prospect of a deal with Labour which would hand Mr Corbyn the keys to Downing Street in exchange for a transfer of power to allow a referendum to take place.
Asked if she believes Labour would grant a Section 30 order, transferring power to Holyrood for a referendum, Ms Sturgeon replied: "Yes."
But there would not be in any formal pacts or Coalitions with Labour after the election, Ms Sturgeon said. as she visited Leith in Edinburgh to support the re-election of Deirdre Brock MP.
"We will judge these issues when we see what we're dealing with after the election," Ms Sturgeon said.
The two leaders met last week, but the prospect of a section 30 order was not raised,
"The discussion I've had with Jeremy Corbyn in recent months have, I think understandably been about Brexit and about the tactics in the House of Commons.
"I met with him - last week was the most recent occasion - that was very much about Brexit and the prospects as they were then of an election.
"I don't think Jeremy Corbyn is under any illusions though about my position around independence, a referendum and the transfer of power.
"I've got many disagreements with Jeremy Corbyn, but UK Labour's position seems to me to be a statement of democracy rather than a denial of democracy which is the position of the Scottish Labour party."
'Fall into line'
But she added Scottish Labour will eventually "fall into line" with the Uk party.
Ms Sturgeon is seeking to hold a referendum next year, but Mr Corbyn has indicated it won't happen in the early years of a Labour Government.
But Ms Sturgeon said: "If you reverse this and think about the alternative and the position that the Tories in Scotland - and, still on the face of it Scottish Labour - are arguing.
"At the start of an election campaign they seem to be saying to people in Scotland we don't care how you vote, we're going to ignore you.
"I would suggest to them that is not the most attractive election position to take. I never have believed this is sustainable. So if people in Scotland demonstrate the desire, as I believe they will in this election, for an independence referendum, then I don't believe Westminster opposition to the principle or to the timetable for that will prove to be sustainable at all.
"Everybody knows, you all know, there's going to be an independence referendum - the opposition parties might not yet have got round to conceding that point in public. But everybody knows."