Sir Keir Starmer will hold in-person talks with John Swinney "to discuss a referendum on independence", according to the Scottish First Minister.
Mr Swinney described the Prime Minister's decision to agree to a face-to face meeting as "particularly welcome".
It has been scheduled for next month - so amid extraordinary pressure for Sir Keir to step down, the First Minister may be meeting someone else entirely.
No10 has so far denied claims that Scotland's constitutional future will be on the agenda, insisting the talks will focus on "shared issues".
The meeting comes after the SNP won its fifth successive Scottish Parliament election, securing 58 seats in Holyrood - but falling short of the 65 required for a majority.
Sir Keir called the SNP leader on Tuesday evening to offer his congratulations on the pro-independence party's victory.
Mr Swinney said the Prime Minister agreed to the meeting after he highlighted that Holyrood now has a record number of MSPs who back Scottish independence.
However, a Downing Street spokesman insisted that Sir Keir made it clear during the phone call that Labour would not entertain a second independence referendum.
Prior to the election, Mr Swinney argued that an SNP majority would give them an "emphatic mandate" to hold another vote.
Sir Keir Starmer will hold in-person talks with John Swinney 'to discuss a referendum on independence'
|GETTY
Though last year, Sir Keir said he could not imagine a second referendum taking place during his stint in Downing Street.
The Prime Minister said at the time that "nobody's raising that with me as their first priority" - remarks which were later blasted as "arrogant" by the SNP.
When asked about a second referendum last month, Health Secretary Wes Streeting told LBC: "We're not having one."
"This country has had enough of chaos," he added.
KEIR STARMER - READ THE LATEST:
The meeting comes after the SNP won its fifth successive Scottish Parliament election
|GETTY
Scottish Conservative leader Russell Findlay blasted the Prime Minister's agreement to hold talks with Mr Swinney as an "extraordinary capitulation" even by his "dismal standards".
He added: "We warned during the election campaign that if Swinney achieved his self-imposed 'mandate' of an SNP majority, Starmer would be likely to surrender to his referendum demands.
"But for Starmer to entertain talks on the subject when the nationalists haven't even met their own target is downright foolish and reckless."
A spokesman for the SNP leader said: "The First Minister is pleased that the Prime Minister reached out to congratulate him on his emphatic election win and that the Prime minister stressed his willingness to work in collaboration with the Scottish Government where possible.
Russell Findlay blasted the Prime Minister's agreement to hold talks with Mr Swinney as an 'extraordinary capitulation'
|GETTY
"Given the SNP's landslide victory and the fact that the people of Scotland have elected more pro-independence MSPs than at any point in the parliament's history, the previous refusal of the UK Government to consider Scotland's right to decide its own future was clearly unsustainable.
"A way forward must be found and so these discussions are welcome."
Meanwhile, a Downing Street spokesman said: "The PM committed to meeting to discuss shared issues including the cost of living.
"As the PM told the First Minister, the manifesto this government was elected on was unambiguous that 'Labour does not support independence or another referendum'."
"Our position remains unchanged."
Our Standards: The GB News Editorial Charter