But the First Minister stopped short of formally joining a Liberal Democrats's campaign for a vote on the final deal when it emerges.
The proposal has widespread support among opponents of UK's proposed EU departure.
Liberal Democrat leader Willie Rennie said at First Ministers Questions today: "Brexit is a shambles and it's damaging the country."
He pointed to weekend comments from Ms Sturgeon's ex-advisors Noel Dolan and Kevin Pringle who backed a a second EU vote and called on the First Minister to back it.
Ms Sturgeon said: "It's not the SNP that's going to be a block if there is second referendum on the EU issue.
"If there's to be any prospect of this it's not the SNP he needs to convince - it's one of the main parties in Westminster that he'll need to convince, given that we can't at the moment seem to even convince the Labour opposition of the case for the single market so I'm not sure there's much grounds for optimism."
Ms Sturgeon has previously said calls for a second vote could become "irresistible" and even suggested she had some sympathy for it.
But there had been doubt about whether the SNP could agree to a second vote - as it would open the door to a future Yes vote in a Scottish independence referendum being overturned by a second vote on the final terms of departure from the UK.
Ms Sturgeon added that Scotland did vote overwhelmingly to "remain" in the last referendum two years ago.
"The problem in Scotland is that our remain vote has been completely ignored - so what guarantees can Willie Rennie give people in Scotland if that was the outcome again that that remain vote would not be ignored in exactly the same way all over again."