The First Minister had set the timetable of a second ballot on Scotland’s place in the UK being held between autumn 2018 and spring 2019 when she announced her plans in March.
But in the wake of the general election, in which the SNP saw its share of the vote fall from 50% to 37% as the party lost 21 Westminster seats, she has been reflecting on that position.
The issue was discussed at the Scottish Government cabinet meeting last week, with Ms Sturgeon “likely” to set out her position before Holyrood goes into recess at the end of June.
The Sunday Mail reported a senior SNP insider as saying that in the wake of the general election - in which the Tories lost their overall majority at Westminster - “doing everything possible to help achieve a soft Brexit for the UK as a whole or Scotland is the priority”.
The insider added: “People can judge on the other side of the negotiations what they want to do about independence.”
A spokesman for Ms Sturgeon said: “Reports in today’s newspapers are entirely speculative.
“We have always made clear our view that the people of Scotland should have a choice at the end of the Brexit process and the First Minister will set out her views on the way forward in the coming days.”
The Scottish Government has been pushing for a second vote on independence to be held to give voters north of the border - the majority of whom voted to stay in the EU - an alternative to Brexit.
Ian Blackford, the SNP’s new Westminster leader, said a key part of his job was working to “get the best deal for Scotland out of Brexit”.
But he also insisted that the party would remain committed to independence.
Mr Blackford, speaking on the BBC’s Sunday Politics Scotland said: “One of the things I think is important is if we’re going into the Brexit negotiations we need to wait and see what the outcome of that is.
“What we have continually said is that the people of Scotland, just like the members of any other European nation.....should be able to have their say on the final outcome of Brexit.
“We need to make sure we can protect the national interests and once Nicola has reflected on the election result, of course we will come forward with our proposals as to how we move forward.”
He added: “What I’m doing is concentrating on the job I have, along with my colleagues at Westminster, which is standing up for Scotland.
“It’s making sure we get the best deal for Scotland out of Brexit, challenging the Tories on austerity and, of course, the SNP is the party of independence.
“What I’ve said is Nicola will make her judgement on what has happened in the election campaign and we’ll make sure we get a very strong message that we take forward for the people of Scotland.”
Mr Blackford continued: “The SNP is the party of Scottish independence and will remain so but what we have to do is to is actually focus on the priorities which are there in front of us today, it’s protecting Scotland’s interests in Brexit, making sure we can deliver an alternative to austerity.”