Alex Salmond’s new Alba Party would win six seats, according to an analysis of the Panelbase poll for the Sunday Times.
The SNP would win a narrow outright majority with 65 seats, with the Scottish Greens forecast to take eight seats.
An analysis of the poll by Sir John Curtice of Strathclyde University put the Scottish Conservatives on 24 seats, Scottish Labour on 20 and the Liberal Democrats on five.
George Galloway could enter the Scottish Parliament as his pro-union Alliance for Unity group may take a single seat.
Panelbase surveyed 1,009 adults in Scotland between March 30 and April 1.
It is the second opinion poll to include Alba since the party was launched by the former first minister to contest the regional list seats.
In the constituency vote, the SNP was on 49%, with the Tories on 22%, Labour on 20% and the Lib Dems on 6%.
For the regional list vote, the SNP was on 39%, with the Conservatives on 21%, Labour on 17%, and the Greens on 8% and the Lib Dems on 5%.
The poll had Alba on 6% for the regional list vote, with All for Unity on 4%.
Writing in the Sunday Times, Sir John said Panelbase’s results were “good news” for the Alba Party, though a drop of just 2% in support would mean their tally would fall to one MSP.
The polling expert said: “Alba may be on the cusp of recording a creditable performance and coming away largely empty-handed.
“Although most of the seats the party could win with a 6% tally look as though they would be secured at the expense of the unionist parties, our projection suggests that a couple might otherwise have been won by the SNP or the Greens.
“Even with an estimated 49% of the constituency vote, that is not a possibility the SNP will regard with equanimity.
“Such a result in the constituencies could still leave the party a seat short of an overall majority and reliant on winning a vital list seat to achieve what has come to be regarded as a crucial target.”
He said that despite Nicola Sturgeon’s call for “both votes SNP”, 9% of those who back the SNP in the constituency vote indicated they would vote Alba on the list and as many as 10% would opt for the Scottish Greens on the list.
He continued: “Alba is appealing to a section of the nationalist movement that wants a rapid timetable for indyref2 and which still admires Salmond.
“As many as 70% of Alba supporters want a referendum within 12 months compared with 48% of SNP list voters and 35% of Green voters.
“While 93% of those who back Alba believe that Salmond is ‘a fit person to stand for election’, only 13% of SNP supporters and 15% of Green voters take the same view.
“Salmond’s personality has enabled him to create a new party out of nothing.
“However, it may now also constrain what the party can hope to achieve.”
Responding to the poll, SNP depute leader Keith Brown said: “This is the most important election in Scotland’s history – every single vote will count, and this poll shows that giving anything less than both votes to the SNP means gambling with Scotland’s future.
“These serious times require serious leadership, and people across the country can put their trust in the experience of Nicola Sturgeon as we move through the pandemic and towards a strong, secure recovery.”
Mr Salmond said: “We have only just begun to make our case, but Alba is already registering as the standard bearer of the Independence #Supermajority.
“The reality that voting SNP on the list is the ultimate wasted vote is starting to cut through. And therefore Alba is gaining ground.
“In a single week Alba has overtaken the Liberal Democrats, a party which has been around for 150 years, in both membership and poll ratings.“A week is a long time in politics. And for the unionist parties, the next five weeks shall be a political eternity.”