Scotland voted to stay in the bloc and Sturgeon has said an independence vote is inevitable unless Britain softens its Brexit plans.
In an interview with the BBC today, Nicola Sturgeon refused to rule out next autumn as a date for a new referendum.
She added: "I'm not ruling anything out".
As Theresa May braces to trigger Article 50, a new poll suggests that 50% of Scots are ready to support independence, while 50% would want Scotland to remain in the UK.
Under the UK's constitutional conventions, an independence vote would have to be approved by May's government which on Thursday (Friday NZT) repeated it saw no need for a second ballot.
The MP and former first minister of Scotland led the party between 1990 and 2000 and then 2004 and 2014, and said he "learned a long time ago to never say never in politics".
The ex-SNP leader made the suggestion after his successor Ms Sturgeon warned the Prime Minister's plan to take the United Kingdom out of the European single market "undoubtedly" makes another vote on the future of the United Kingdom more likely.
This was echoed by Scottish Labour leader Kezia Dugdale who said that it was "another attempt by Nicola Sturgeon to sow division and uncertainty, at a time when the country needs to pull together more than ever".
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Mrs Sturgeon has repeatedly claimed time is running out for the UK Government to present a Brexit deal which would let Scotland stay within the single market, even if the rest of the country leaves.
Harvie said there have been "informal" discussions between the Greens and the SNP about the possibility of another independence referendum, but that it was too early to talk about what the campaign might look like this time.
But he said: 'The question is should there be a second referendum, and we don't believe there should.
She has warned repeatedly that she will not allow Scotland to be taken out of the European Union against its will.
"Both sides agreed to abide by that and we think both sides should".
Of course under the constitution it's up to Theresa May, the Prime Minister, to decide when - and whether - to allow another Scottish referendum.
Although the Government could deny the legal authority for another referendum, that decision could threaten the stability of the union.
But while in principle the Westminster position is that the last independence referendum, in 2014, settled the matter for a generation, in practice, May would be unlikely to refuse.