The Strathclyde University professor told BBC Radio Scotland's Good Morning Scotland programme on Friday that polls currently put the SNP on around 40% of the vote, while Labour has dropped to 20% north of the border.
His comments come at the end of the first full week of official campaigning ahead of the December 12 General Election.
Sir John said: "The SNP look as though they're around 40%, which is about three points up on where they were in 2017, so they're at least holding on, probably going up.
"The polls are very clear, unsurprisingly given the state of the Labour Party's poll position in the UK as a whole, that they are well down in Scotland - probably heading for around 20% of the vote and therefore down seven, eight or nine per cent.
"A slight question mark over the Conservatives, recent polls still had them down about seven points in Scotland, but given they have been making some ground across the UK as a whole and there's something of a Brexit Party vote to squeeze in Scotland, it would be surprising if the Conservatives were not at risk of losing some of their seats."
The professor also claimed it is a "widespread misapprehension" that Labour voters are not in favour of Scottish independence.
He said: "If you look at the polling evidence in Scotland, sure, a majority of Labour voters in Scotland are in favour of staying inside the union.
"But the polls consistently find in the high 30% of those who say they are going to vote Labour, are in favour of independence.
Challenge for Labour
"The Labour Party have always been the centre party on the constitutional question in Scotland, it is still the centre party on the constitutional question.
"As a result, it tends to draw support from both sides of the spectrum, but it does leave the party with something of a dilemma about how it keeps these groups together.
"In the 2015 election it lost a large chunk of its independence supporting supporters.
"As compared with the Conservative Party, Labour's vote in Scotland is very different. The party is much more able to pick up votes from independence supporters than the Conservatives.
"That said, the Labour Party doesn't look like it's going to have enough voters in either camp to look like it's going to be a credible challenger."