The party are demanding a more representative discussion, featuring more voices than just those of the Labour party and the Conservatives.
Keith Brown, the SNP’s Depute Leader, stated that in order to give people the chance to properly discuss and scrutinise “all of the options that are being put forward” – including the SNP’s position for the whole UK to maintain membership of the Customs Union and Single Market in order to protect jobs and the economy - more voices must be included, he said: “Sky News are right to look to stage a televised Brexit debate, but wrong to want to host a head-to-head debate between May and Corbyn.
“The idea that this is a binary choice between a Tory hard Brexit or a Labour hard Brexit is grossly misleading.
“Labour and the Tories only reflect the views of a limited share of the British public – and an even smaller share of Scottish public, who voted overwhelmingly against Brexit – so it would be a massive mistake for a live leaders’ debate to go ahead without Nicola Sturgeon.
“As other broadcasters have noted, the First Minister of Scotland needs be involved if there is to be a truly representative televised debate.”
The SNP’s defence spokesman Stewart McDonald said his party must be included, claiming a debate between Mrs May and Mr Corbyn “would represent the worst type of Westminster carve-up”.
He tweeted: “Any TV debate that takes place on Brexit must include all parties represented in the UK parliament.”
A spokesman for Downing Street refused to confirm whether Number 10 was considering such a debate.
He told reporters on Monday: “The Prime Minister debates the leaders of the opposition parties regularly on Brexit and will be doing so in effect at 3.30pm today (when she makes her statement to the House of Commons).”
The Lib Dems, the Green Party and Plaid Cymru have also said that they should be involved.
Liberal Democrat leader Sir Vince Cable demanded to be involved because neither the Tories nor Labour had called for a second Brexit referendum.
The Greens have also said they must be included, saying any debate “must be cross-party, featuring a diverse range of voices representing every nation, as well as every stance on this deal and our relationship with the EU”.
Plaid Cymru leader Adam Price tweeted: “People deserve the opportunity to hear from all the different voices on the biggest decision we will make for generations.
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“I’m ready to make sure Wales’s voice is heard in any TV debate.”
The PM was accused of “running scared” last year after refusing to appear at any of the TV debates in the run-up to the snap General Election.
But she is embarking on a PR blitz this week as she tries to convince the public to back her Brexit deal and put pressure on MPs to support it as it goes to a vote in Parliament.
Campaigners seeking a second referendum have written to broadcasters, saying that a head-to-head debate would breach impartiality rules.
The People’s Vote campaign said excluding a candidate who backs a new poll would be in breach of the BBC Charter and Ofcom rules on fairness in political broadcasting.
In a letter sent to BBC director-general Lord Hall, ITN chief executive John Hardie and John Ryley, the head of Sky News, they said: “A format agreed hastily between Downing Street, the office of the leader of the Opposition and broadcasters would damage the reputation of TV debates, as well as perhaps, British broadcasting in general.”