The results follow SNP figures rejecting the possibility of a three-option ballot paper earlier in January, with Scottish Government minister Kevin Stewart branding the suggestion “idiotic, foolish, nonsensical” and MSP Gillian Martin rejecting it as a “con”.
The debate around devo-max, which has been promoted as a solution by parts of the Labour movement for years, was reignited following comments from former SNP policy chief Chris Hanlon.
It also comes ahead of the former Labour leader and Prime Minister Gordon Brown’s commission on the future of the union, expected to be published later this year and likely to form a central part of Labour’s strategy for the union.
The poll, undertaken by Savanta ComRes for Scotland on Sunday interviewed 1,004 Scottish adults aged 16 or over between January 14 and 18.
It showed that when devo-max was defined as “full fiscal autonomy”, meaning the Scottish Parliament would receive all taxation raised in Scotland and would be responsible for the majority of public spending other than defence and foreign affairs, Scots tended to reject the concept.
Just 26 per cent – just over a quarter – of Scots would support the concept of devo-max, the poll showed, with just four per cent “strongly” supporting the concept.
The majority of Scots also said they did not want to see a three-option referendum should there be another independence vote.
In total, 55 per cent of Scots said they would prefer a two-option ballot paper, similar to that used in the 2014 independence referendum.
Almost a third, 32 per cent, said they would back a three-option ballot if it included devo-max as an option, while 14 per cent said they did not know.
Of the three main Scottish parties, Labour voters are most likely to back a three option ballot paper, with 37 per cent stating they would back it and 48 per cent opposing the idea.
However, SNP voters were most likely to back the concept itself, with 27 per cent “somewhat” supporting it and five per cent “strongly” supporting devo-max, compared to 23 per cent and six per cent respectively among Labour voters.
Devo-max was overwhelmingly rejected by Conservative voters, however, with 55 per cent saying they would oppose the concept, including 29 per cent “strongly” opposing it.
More Scottish voters believe devo-max would be a bad compromise (39 per cent) than a good compromise (32 per cent), however a third (29 per cent) said they did not know whether it would be worthwhile for Scotland.
The concept was rejected most strongly by Conservative voters, with 59 per cent arguing it would be a bad compromise, compared to 38 per cent of SNP voters and 34 per cent of Labour voters.
Just 23 per cent of Tory voters would say devo-max is a good compromise, compared to 32 per cent of SNP voters and 37 per cent of Labour voters.
Chris Hopkins, associate director of Savanta ComRes, said promoting devo-max could hurt the unionist cause.
He said: “Devo-max may be a concept that many Scots struggle to get their head around: indeed, a third (29 per cent) say they don’t know whether or not the concept is a worthwhile compromise, and a similar proportion say they feel neutrally on whether they support or oppose it.
"Ultimately, while those banging the drum for devo-max may be well-intentioned, we’ve seen before that further complicating divisive issues in Scottish politics doesn’t always lead to better outcomes for your cause – something that the Alba Party, with their desire for a “supermajority”, may be all too familiar with – and it may be that watering down independence with end up satisfying nobody, and causing fractures among pro-independence voices.”
SNP MSP Gillian Martin said: “The people of Scotland elected a majority to their Parliament with a clear manifesto commitment to hold a single question referendum – more seats than the mandate won in 2011.
"No form of devo-max would have prevented Scotland being dragged out of the EU against our will or the Tory power grab on Holyrood – only independence can fully protect our national interests.”