The SNP is to announce its new Westminster group leader later.
According to the newspaper, a third (34%) of those who voted Yes in the 2014 referendum on independence told pollsters the First Minister should drop the proposal.
Edinburgh's call for a special deal to keep Scotland in the single market while the rest of the United Kingdom leaves the bloc has been repeatedly rejected by the British government.
Nicola Sturgeon was today forced to deny reports she is secretly plotting to hold another Scottish independence referendum - despite the SNP's staggering election losses.
Sturgeon said on Monday that the disappointing results last week had left the United Kingdom government so unstable and weak it was vital that the British premier sought the support of devolved governments and opposition parties to adopt a common position before London started negotiations with Brussels.
The SNP leader said she would "reflect" on the result and "listen" to Scots following the general election.
Varadkar confirmed as Ireland's first gay prime minister
The Fine Gael TD is switching from Foreign Affairs to Justice Minister, as part of new Taoiseach Leo Varadkar's reshuffle. In 2015 , Varadkar said his sexuality, like his ethnicity, "is not something that defines me".
She wrote: "During the election you sought a mandate for your proposals to leave the European Single Market".
Nicola Sturgeon has called for Theresa May to pause the Brexit negotiations to build a new cross-party, "four-nation" consensus on the UK's stance with the EU.
The SNP has insisted the donation page was shut down so the party could focus on raising funds for the general election, but analysis from BuzzFeed News suggests the page was live as recently as last Thursday - the day of the election.
The First Minister has previously admitted the issue of another independence ballot was a factor in the election and stated the party will reflect on its plans amid calls for it to be taken off the table. It will not be possible for the United Kingdom to effectively implement the outcome of the Brexit negotiations without the co-operation of devolved governments. "It is therefore essential that we are part of the negotiating process".
Ms Sturgeon said: "Now that the Queen's Speech has been postponed, questions have been raised about what has been cooked up behind closed doors and is it possible for this Prime Minister - notwithstanding what she said on Friday - to put together a Government that is functional and sustainable".
Ms Sturgeon's letter follows interventions from across the political spectrum, including her Welsh counterpart Carwyn Jones and former PM David Cameron.
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