Speaking on the findings, Ipsos Mori Scotland director Mark Diffley, said: "In the immediate aftermath of the EU Referendum vote last June there was an increase in support for independence, which ebbed away later in the year".
"I think [that] would be the common sense time for Scotland to have that choice, if that is the road we choose to go down", Sturgeon told the BBC's political editor, Laura Kuenssberg.
"I'm not ruling anything out".
The SNP leader once again pushed the blame to Westminster, insisting she was met by a "brick wall" while trying to negotiate Scotland's standing in the EU.
Less than a fifth (17%) said an independent Scotland should not be in either the European Union or have access to the single market while 8% either did not know or refused to answer.
No 10 has dismissed the possibility of a second referendum on Scottish independence, saying continued talk over the issue is just a "distraction".
However since then the United Kingdom voted to leave the European Union despite 63% in Scotland wanting to Remain, prompting Sturgeon to say another referendum is "highly likely" after the vote.
There is speculation that Sturgeon may announce a second referendum at the SNP conference next weekend (17-18 March).
In January, former first minister Alex Salmond said a vote on Scottish independence could take place in autumn 2018.
She also spoke of how there had been no final decision made on whether such a vote would be held.
"Common sense would tell you that. if we are going to become independent, better to do so before we are dragged out of the EU", Stewart Hosie, an SNP lawmaker said.
Pressed on the timing of a second referendum by the BBC, she said she was "not ruling anything out".
Scotland has been pushing to remain inside Europe's single market - even if the rest of Britain leaves - and Sturgeon has called on May to agree to a deal that would allow the nation of 5.4 million to maintain key components of European Union membership. I suggested that Sturgeon's sense of urgency might be explained by opinion polls showing her "tanking" approval rating.
Ms Sturgeon strongly disagreed with Mr Gove's views, instead pinning her desire for independence on the Prime Minister's pandering to the Conservative's right-wing contingent's calls for a "hard" Brexit.
Overall, Britain voted by a margin of 52 to 48 percent past year to quit the 28-nation bloc " but voters in Scotland voted by 62 percent to 38 percent to stay in.