Sir John Curtice, professor of politics at the University of Strathclyde, also said he expected to see the Conservatives lose ground in what will be a fascinating test of public opinion a year on from the Holyrood election.
The council elections, Covid permitting, will take place on May 5 later this year, and will test whether the SNP can continue to perform well at a local and a national level.
It will come as Nicola Sturgeon prepares to lay the groundwork for a second independence referendum, while local politicians in the North East will highlight the move away from the oil and gas industry.
Sir John said the local elections were also the last chance for the Alba party, run by former SNP leader and first minister Alex Salmond, to make an electoral breakthrough.
The polling expert said given the SNP’s disappointing performance in 2017, just weeks before it lost ground in the snap general election held by Theresa May’s government, Ms Sturgeon’s party should improve.
The party ended the council elections in 2017 leading eight councils with a minority administration, while joining a coalition across seven other councils.
This was despite polls suggesting the SNP would make substantial progress at those elections.
Sir John said the relative strength of the Conservatives in 2017 against Douglas Ross’ party’s position in the polls today means the SNP should make gains.
He said: “Given that the standing of the Tories is quite considerably down from where it was five years ago, and the SNP, while 2017 is obviously a warning that it won’t necessarily be as good as the polls, but even so the way that the SNP are running around 48-49 per cent, they were at 43 even in the polls that were exaggerating their position in 2017.
"The SNP ought to have done this last time. They certainly ought to this time, to record their best set of local election performances since the advent of STV.
"This is a relatively sticky wicket for the Tories. It’s an occasion which the SNP should be making notable gains.”
In 2017, then led by Ruth Davidson, the Tories sat at around 25 to 30 per cent in the polls and received around 25 per cent of the first preference vote, winning 276 seats and becoming the second biggest party in local politics in Scotland.
This also presents potential opportunities for Labour to win back some of the support it lost in 2017 when it conceded a third of its total vote share.
However, Sir John says Anas Sarwar’s party and the Scottish Liberal Democrats would both likely tread water.
He said: “Around spring 2017, we were beginning to ask the question could the Tories become the dominant party of unionism, could they begin to consolidate the unionist vote and then they failed to do so.
"Labour might tread water because they are running at around 21 per cent in the polls. The Liberal Democrats look like they will tread water.”
The SNP’s new partner in central government is the “big uncertainty”, Sir John said, with the Greens’ success depending on where they stand and whether they eat into the SNP support in key areas such as Glasgow and Edinburgh.
He said: “They may well puncture some of the gains the SNP might hope to make because it is pretty clear that the Greens and the SNP are basically fishing in the same water because everything now is so heavily polarised by people’s constitutional preference.
"The Greens may well clear the pitch for the SNP to some degree, but probably only to some degree.”
Mr Salmond's new party, Alba, has been polling consistently at or below 2 per cent since the Holyrood election in May, with Sir John stating this was the party’s last chance at a breakthrough.
As it stands, the party has 15 local councillors all of whom defected to Alba from other parties, but the polling expert cast doubt if any would be returned in May.
He said: “The difficultly for Alba is although we’ve got a proportional electoral system, it is not very proportional.
"You’ve got to be getting about 20 per cent of the first preference vote to be sure of getting a seat in a four-member ward. Even allowing for transfers, you’ve got to be getting 15 per cent plus.
"Maybe somebody, somewhere will manage it, but they have got to be registering far more than they have done in any polling so far before they are going to make any breakthrough in these local elections.”
Sir John said it was likely the SNP would win back control of Dundee City Council, which it lost in 2017, and could tackle the unionist coalition administration of Labour and the Conservatives in Aberdeen.
He also predicted the SNP was likely to remain in control of a minority administration in Glasgow and potentially helped to a majority with additional Green councillors.
Meanwhile, the Scottish capital’s council is set to be a question of who is ready to do a deal rather than any one party winning out.
Sir John said: “Nobody is going to get a majority in Edinburgh, thereafter it becomes a question partly of numbers and who is willing to do a deal, but the Tories are likely to go down. They did very well in 2017 and they are likely to lose ground.
"Broadly speaking the Greens should be making progress and given in Edinburgh and in Glasgow we know that they can get close to the quota in a fair number of wards.
"If they can get themselves over the quota in a few more wards, it is really looking for those wards where they weren’t far off last time, involved in the last count and just didn’t make it, those are the ones to look for to see how many of those there are to get an idea to whether or not they might make it this time.”