Scotland’s First Minister said the scenario, alongside speculation around taking legal action to try to secure another referendum, was not one she had in mind.
Ms Sturgeon has said she will set out her next steps to the Scottish Parliament following the Easter recess after MSPs voted by 69 to 59 in favour of seeking permission for another vote.
The Scottish government insists a second referendum is needed to give Scots a choice between Brexit and independence, but the Prime Minister has repeatedly said “now is not the time”.
The First Minister told BBC Radio Scotland’s Good Morning Scotland programme: “I’m absolutely clear that the position of Theresa May I just don’t think is politically sustainable.
“If the Scottish Parliament is of the opinion, as it is because it has voted in this way, that Scotland should be given a choice, not now, but when the time is right, when there is clarity about Brexit and when obviously there is clarity also about independence, that we should have a choice about our future.
“Having written to Theresa May on the back of the Scottish Parliamentary vote, I’ve said some time after the Easter recess I will set out what I consider the next steps to be, but I will set that out to parliament.”
Addressing the options of court action or a snap Holyrood election, she added: “These are not the kinds of things I am thinking of. I was elected as First Minister just less than a year ago. I’ve got a responsibility to lead this country.
“We are very focused on getting growth in our economy and transforming education. These are things that continue to be my priorities.
“But I also think it’s right that at the right time Scotland doesn’t have our future direction as a country imposed on us, but that we get to choose that.
“These sort of scenarios that are put to me are not the ones I am thinking of, but I do have an idea of how we progress the will of parliament.”