A survey by Savanta for The Scotsman suggests 31% of Scots could vote Labour on Thursday, three points down on the last poll, while support for the SNP is unchanged at 34%.
According to analysis from Professor Sir John Curtice, Labour, which won just one seat north of the border in the 2019 election, is on course for 22 Scottish MPs while the SNP would keep 24 seats.
The poll, carried out between June 28 and July 2, suggests the Conservatives are on 15%, up one point, while the Liberal Democrats are at 9%, up two points on the last poll earlier in June.
The latest poll of 1,083 Scottish adults found 6% said they would back Reform UK, no change since the last poll, while the Greens were up one point at 3%, and 2% said they would vote for other parties.
If our results were reflected on polling day, John Swinney's election as SNP leader looks like it will have come just in the nick of time
Chris Hopkins, political research director at Savanta, said: “Our final Scottish voting intention before 4 July suggests the SNP is ahead of Labour, showing a modest improvement and potentially blunting their losses on election night.
“If our results were reflected on polling day, John Swinney’s election as SNP leader looks like it will have come just in the nick of time.
“That being said, Labour’s efficient vote, in particular around the central belt, will still mean it’s likely going to be a very good evening for Anas Sarwar and Keir Starmer.
“Their majority is no longer dependent on Scotland, but they’ll want to squeeze the SNP as much as they can.”
Savanta’s poll also suggests the SNP, unchanged at 37%, is ahead of Labour in the Holyrood constituency voting intention, with the latter at 32%, down three points on the last poll.
The poll puts the Conservatives on 16%, up two points, while the Liberal Democrats are on 9%, up one point, with 6% saying they would vote for others, up one point.
The Holyrood list vote was much closer, with the SNP on 29% (down two points), Labour on 28% (down one point) and the Conservatives on 16%, also down one point.
The Greens were on 11%, up two points, the Lib Dems on 11%, also up two points, and support for “other” was at 5%, up one point.
Analysis by Professor Curtice suggested that if these results were reflected at election time, the SNP would remain the largest party in Holyrood with 46 MSPs.
The Labour Party would be a close second with 37 MSPs, and the Conservatives would be reduced to 21 MSPs.