The Panelbase survey for the Sunday Times suggests that Ian Murray will be returned as the only Scottish Labour MP, while Stirling’s Stephen Kerr would be the only Tory to lose his seat.
Analysis of the poll by Strathclyde University Professor Sir John Curtice says the SNP could expect to win 41 seats on election night, with the party losing North East Fife to the Liberal Democrats.
Panelbase puts the SNP on 40%, the Tories on 28% - up seven points in the past month, Labour on 20%, and the Liberal Democrats on 11%.
The poll surveyed 1,009 people in Scotland, and found the First Minister to be the only leader with a positive approval rating at +3%.
Prime Minister Boris Johnson's popularity rose slightly from -36% to -34%, while the Labour leader also improved but still found himself trailing the Tory leader on -41%.
On the issues voters believe to be harmful to the UK, 37% of Scots said Scottish independence, with 39% saying the same of Brexit.
Almost half of all those surveyed said Scottish independence would be a "good opportunity" for the country, at 45%, while just 24% said the same of Brexit.
Responding to the poll Kirsty Blackman, the SNP's deputy Westminster leader, said: "Only the SNP can beat the Tories in Scotland.
"While we take nothing for granted, the SNP are in a strong position - and we're well and truly the party with the momentum.
"This poll underlines the fact that neither Labour nor the Lib Dems can take seats off the Tories.
"Boris Johnson is desperate to get a majority, force through a disastrous Brexit and inflict yet more years of Tory misery on Scotland.
"The only way to stop him is to unite around the SNP and help lock him out of Downing Street."
Mr Kerr said: "We welcome today's poll.
"It confirms that, in seat after seat in Scotland, it's only by voting Scottish Conservative that people can stop Nicola Sturgeon and make her listen.
"By contrast, the poll shows that Labour is going nowhere in Scotland and that it now risks being completely wiped out.
"So our message to Labour and Liberal voters today is to lend us your vote so together we can beat the SNP.
"We did it two years ago - let's do it again."