The Panelbase survey for The Sunday Times and LBC puts backing for independence at 44%, one point lower than when the question was put to Scotland two-and-a-half years ago, while a majority (56%) would vote to remain in the United Kingdom.
The poll of 1,008 voters in Scotland was conducted between Monday and Friday following confirmation from Ms Sturgeon that she will seek permission to hold a second vote on the issue.
Ms Sturgeon told delegates at the SNP conference in Aberdeen she was willing to negotiate ‘’within reason’’ on the timing of any ballot after Theresa May dismissed the call saying “now is not the time”.
The poll suggests a majority of Scots agree with the Prime Minister, with 51% saying they do not want another referendum to take place in the next few years.
Almost a third (32%) supported having a referendum in the next year or two while the Brexit negotiations are ongoing, while around 18% backed another ballot about two years from now when negotiations are complete.
However 44% said they expected one to take place within the next five to 10 years, up six points since Panelbase asked the question in January, and nine points since last September.
John Curtice, professor of politics at the University of Strathclyde, told the newspaper: “The First Minister has not had any success at all in reducing the level of opposition to holding any kind of referendum in the wake of Brexit.
“The Yes side still has considerable ground to make. More time to argue her case might, in truth, be just what Nicola Sturgeon wants.”
On the economics of independence, just 13% of those surveyed thought it would make them at least £500 a year better off, 34% believed they would be at least £500 worse off, 28% said it would make little difference and 25% did not know.
Asked who they would vote for in a Westminster general election, 47% backed the SNP, support for the Scottish Conservatives was at 28%, Scottish Labour was on 14%, the Lib Dems on 4% and the Greens and Ukip both on 3%.
Meanwhile a poll for The Independent found that 44% of respondents in Scotland agreed with the statement: “Theresa May should insist that any second Scottish referendum on independence takes place only once Britain has concluded the process of leaving the EU.”
However 48% disagreed, while 8% said they did not know.
In England and Wales 60% of respondents said Theresa May was right to refuse a second referendum while negotiations with the 27 other EU states are under way, while 21% said she was wrong.
The poll of 2,026 adults, including 185 in Scotland, was carried out by ComRes online between March 15 and 17.