The Prime Minister is facing legal challenges over whether she has the right to begin the Brexit process without the approval of Parliament, The Press Association reported.
But the Daily Telegraph reported she had been told by government lawyers that she did not need parliamentary approval to begin the Article 50 procedure, which starts a two-year countdown to cutting ties with Brussels.
A Downing Street source said the report was speculation but added that Mrs May was “committed to delivering on the verdict the public gave”.
Labour leadership hopeful Owen Smith has promised to attempt to block the triggering of formal negotiations to leave the EU until the Government offers a second referendum or calls a general election to approve its final Brexit deal.
He said that under his leadership the Labour Party would opposed triggering Article 50 until the Conservatives commited to a second public vote.
A legal challenge bid to prevent the Government from triggering Article 50 of the Lisbon Treaty without the prior authorisation of Parliament is due to be heard in the High Court in October.
Government lawyers are expected to assert that the Prime Minister can use the royal prerogative to start the process of withdrawing from the EU.
Those mounting the challenge say the course proposed by the Government is unlawful because only Parliament is empowered to authorise service of the Article 50 notice and consequent withdrawal from the EU.
Meanwhile, former Tory leader Iain Duncan Smith has suggested Britain could rely on World Trade Organisation (WTO) rules to trade with the European Union (EU) following Brexit.
The prominent Brexiteer said the UK should not necessarily seek to remain a member of the single market as such a move would involve surrendering control to Brussels.
He also predicted the Government will trigger Article 50 early in the new year and start the formal two-year countdown to Britain leaving the EU.
Mr Duncan Smith told the BBC Radio 4 Today Programme that European countries including Germany are eager to negotiate a trade agreement with the UK.
He said: “I think we would like to have, and I think it would be in the interests of the European Union even more than it might be for the UK, to maintain a trading relationship with the UK.
“Bearing in mind that we will anyway have access to the marketplace under WTO rules, so the question really is - do we want more preferential arrangements than that?”
Asked if he would be happy with WTO rules, he said: “I’m saying that’s the extent of where you could be and you’d still get access to the marketplace.
“I’ve already made it clear that my personal view is we should not seek to remain a member of the customs union nor necessarily remain a full member of the single market, because that would entail putting yourself yet again under the rule of European law.
“And that was one of the key areas that the British public voted for in the process of taking back control.”