She said they may be forced into one if there is a hard Brexit
Ms Sturgeon had previously indicated that a "soft" Brexit could take the issue of a second referendum on Scottish independence off the table for the foreseeable future.
However, in a recent interview with the BBC she said she was prepared to call a fresh vote if the terms of Brexit were not right for Scotland.
She said "They will be making a big mistake if they think that I'm in any way bluffing." She continued saying that leaving the European Union created a "fundamental question" for Scotland.
Asked if she was looking at a referendum "much quicker" than in five or ten years' time if there was a hard Brexit she said "I would think, yes. But let me not get away from this point, I'm putting to Theresa May a compromise solution."
She said instead of "prioritising " the "sensible solution" of keeping the UK in the single market, Ms May was just trying to "appease" Eurosceptics in her "deeply-divided" party.
Sturgeon finished by saying "If the UK's coming out of the European Union that has enormous implications for Scotland as it does for other parts of the UK, it has enormous implications for our economy, for jobs, for living standards, for trade, investment, for the kind of society we are."