A spokesman for the First Minister revealed that Ms Sturgeon wanted the Scottish Parliament to be in session when the next Brexit deadline is reached.
MSPs were expected to be out of Parliament for Easter recess from April 8 to 19, but April 12 is the next potential Brexit date.
Today SNP parliamentary business manager Graeme Dey MSP asked for the agreement of the Scottish Parliament's business bureau, including opposition parties, for Holyrood's recess to be vetoed.
A Scottish Parliament spokesperson said: "The Bureau considered the issue at its meeting today and will be considering it further before the close of business on Thursday."
The demand by the First Minister comes after the third defeat of Theresa May's Withdrawal Agreement last week and the failure of any of indicative votes to win a majority last night in Westminster.
In the absence of an agreement to further extend the Article 50 process, and despite MPs voting against a “no-deal” Brexit, the UK will leave the EU on April 12 without an agreement settling citizens’ rights, its financial liabilities, the Irish border issue and without any transitional framework in place.
A spokesman for the First Minister said: "The First Minister's view is that if we're in the same position this time next week as at the moment, facing a no deal, then it would be unacceptable for the Scottish Parliament to be in recess.
"The First Minister and the Cabinet's view is we can't be in a situation where we are on the cliff edge of a no deal with Parliament being in Easter recess. The priority is not recess it's dealing with Brexit."
He added: "We're in pretty grim territory at the moment with no deal being the default option in ten days time. MSPs should not be on holiday when the biggest and most momentous and damaging issue to hit Scotland and the UK since the second World War is about to take place.
"The key point is MSPs should be doing their job. If we are staring down the barrel of a no deal, members of the public would find it weird if Parliament was in recess and not focused on Brexit."
The House of Commons February recess was previously cancelled and yesterday Leader of the House, Andrea Leadsom announced Easter recess will also be axed.
But Scottish Green MSP Ross Greer hit out on social media at the idea recess was a holiday for MSPs. He wrote on Twitter: "Dear First Minister's spokesman, recess isn't a holiday. Its the chance to catch up on all the community work we don't get the time for when parliament is sitting. You know that. Spinning something else won't help you win over MSPs to this proposal."
However a spokesperson for the Scottish Greens added: “Clearly, given the potential consequences of a no deal Brexit, it is quite right that Parliament sits next week, in order that it can appropriately hold government to account in the face of this unprecedented crisis.”
And Maurice Golden, Scottish Conservative Chief Whip, said: “If there’s a genuine reason for Parliamentarians to scrutinise government decisions or legislation next week then of course the Scottish Conservatives will consider supporting it and attend Parliament as appropriate.”
Scottish Liberal Democrat Alex Cole-Hamilton MSP added: “In the event of no deal there will be a lot of frightened people out there and with good reason. They will need reassurances that their representatives are dealing with any issues that arise in a focused and collaborative way.
"Should it come, this will be a time of national crisis the likes of which has rarely been seen. Parliament needs to speak with one voice on resilience planning and will need regular updates on such measures from the Scottish Government.”
The Scottish Labour Party did not comment.