A YouGov poll commissioned by The Times Scotland found that support for Nigel Farage’s party stands at 13%, putting it in third place.
The SNP has also seen its ratings increase from 29% in the 2014 contest to 40% in the survey, ahead of the looming elections for MEPs in the Strasbourg parliament.
However, pollsters found support for Labour has fallen to 14%, compared with almost 26% in 2014.
And the survey suggested that backing for the Conservatives has dropped to 10%, down from their 17.2% share of the vote almost five years ago in the European elections.
The findings - if next month’s election actually takes place and the results were replicated at the ballot box - could see the SNP having three or four of Scotland’s six MEPs.
Elections expert Professor Sir John Curtice told the newspaper that the SNP and Tories would be tied for the final MEP place in such circumstances.
The outcome could also see Labour drop from two MEPs to one while the Brexit Party would pick up the other seat, The Times Scotland said.
The poll also recorded growing support for Scottish independence, with 49% of Scots preparing to vote Yes, compared with 45% in YouGov’s poll for the newspaper last summer.
The findings were published days after First Minister Nicola Sturgeon told the Scottish Parliament there should be another vote on Scotland’s place in the UK before the next Holyrood elections in May 2021.
YouGov interviewed 1,024 people on Tuesday, Wednesday and Thursday this week.