The Scottish government wants to hold a referendum in the autumn of 2018 or the spring of the following year.
However, her call for a second referendum took some analysts by surprise and the previous thinking was that she would only call for a second one, if the polls showed a lead of more than 10 percent for independence.
The UK is now expected to leave the European Union on 29 March 2019.
The government is expected to win Wednesday's vote with the support of the Scottish Greens.
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"Next week, in line with the mandate secured at last May's election, we will ask the Scottish Parliament to agree that the Scottish people should have the right to choose our future".
The motion says it would be for Holyrood to decide the timing and question for a referendum, and to set out who would be eligible to vote in it. The UK's Brexit deal has to be agreed within 18 months, that takes us to Autumn 2018.
But Ms Sturgeon has indicated she would be prepared to discuss the timing of another vote with the prime minister.
Sturgeon will this week call for the Scottish Parliament to set in train a second referendum, largely based on her election manifesto, which stated: "The Scottish Parliament should have the right to hold another referendum... if there is a significant and material change in the circumstances that prevailed in 2014, such as Scotland being taken out the European Union against our will".
She added: "The sovereign right of the people of Scotland to determine the form of government best suited to their needs is a longstanding and widely-accepted principle". I have chosen to put the people in charge.
Tim Farron, leader at Westminster of the Liberal Democrat Party, said May had "rushed this through without a plan, and without a clue".
Members of the Scottish Parliament will debate the motion on a new referendum on Tuesday and Wednesday before holding a vote.
A spokesman in Edinburgh for Scotland's First Minister Sturgeon said: "The fact the United Kingdom government failed to properly and fully inform all of the devolved administrations on the plans for triggering Article 50 speaks volumes, and totally exposes as empty rhetoric Westminster's language about equal partnership".