The Scottish First minister said the question of whether Article 50 could be revoked was becoming ‘pertinent’.
The comments came as pro-EU politicians from across parties mobilised to exploit the fallout from the PM’s disastrous election.
Vince Cable, likely to be confirmed as the new Lib Dem leader next week, said over the weekend that he now believed there was a chance Brexit would not happen.
Miss Sturgeon has previously limited herself to demanding that Scotland is allowed to stay in the EU single market.
But she went further today as she waded into the row over UK membership of Euratom, the European nuclear power agency.
Mrs May has insisted Britain cannot stay in the group because it would mean accepting the jurisdiction of the European Court of Justice.
However, responding to a discussion on Twitter about whether staying in Euratom would require reversing Article 50 process – which means we will leave the EU by March 2019 – Miss Sturgeon tweeted: ‘Is the legal question of whether or not Article 50 could be revoked becoming more pertinent? Still hypothetical – but perhaps less so?’
The government insists that Article 50 is irreversible, although the EU has been less clear about whether it could be overturned.
In theory it means the UK will simply cease to be a member of the bloc in March 2019 – whether or not a deal has been struck.
Foreign Secretary Boris Johnson upped tensions with Brussels today by suggesting European leaders can ‘go whistle’ if they expect Britain to pay a divorce bill for withdrawing from the European Union.
Facing questions over the UK’s future after Brexit, Mr Johnson also told MPs that the Government had ‘no plan for no deal’ because of its confidence over securing a strong Brexit settlement with the bloc.
Mrs May has been struggling to get her government back on track after voters stripped the Tories of their overall majority in the election.
Jubilant Remainers have insisted the result was partly down to anger about Brexit.