The Panelbase survey found that Scots backed independence over No Deal by 52% to 48%, while they backed independence over Theresa May’s deal by 53% to 47%.
The results were published on the same day the prime minister’s spokesman confirmed that a Brexit vote will go ahead in the Commons on Tuesday.
Downing Street was unable to say whether MPs would be deciding whether to formally approve Mrs May’s deal with Brussels.
SNP Depute Leader Keith Brown said: “Brexit, on any terms, is deeply unpopular in Scotland – and the Tories are running scared of giving Scotland a say in our own future.
“The Tories say that Brexit is like hitting an iceberg – and that Scotland has to go down with the ship. It’s time Scotland took its own decisions instead.
“The European Union is a market of 500 million people – eight times the size of the UK alone. Yet the Tories want to drag us out of the world’s richest market against our will.
“No wonder independence is looking more and more attractive.”
Meanwhile, pro-Union campaigners have dismissed an initiative headed by former SNP MP George Kerevan which calls on Nationalists to adopt a bolder approach to establishing a separate Scottish currency after independence.
Pamela Nash, chief executive of Scotland in Union, said: “The SNP’s plan to ditch the pound and put mortgages, pensions and salaries at risk is reckless, and this splinter group now wants to impose the pain on the people of Scotland even earlier.
“The splits within the movement to leave the UK are growing because there is no coherent currency proposal for an independent Scotland, just like Alex Salmond found in 2014.”