The Sunday Telegraph quoted a Downing Street source to say that May had "gone for the full works".
"People will know when she said 'Brexit means Brexit' she really meant it," said the source, described as "familiar with the prime minister's thinking".
May is widely expected to say that the UK could pull out of the European Union (EU) single market and the customs union in order to regain control of immigration and end the jurisdiction of the European Court of Justice in its negotiations over the country's exit from the 28-member economic bloc.
An excerpt of the speech reads: "We need to get on and make Brexit happen. We need to put an end to the division and the language associated with it - leaver and remainer and all the accompanying insults - and unite to make a success of Brexit and build a truly global Britain.
"One of the reasons that Britain's democracy has been such a success for so many years is that the strength of our identity as one nation, the respect we show to one another as fellow citizens, and the importance we attach to our institutions, means that when a vote has been held we all respect the result.
May and her closest aides are believed to be working on the speech throughout the weekend and will reveal its contents to the Cabinet on Tuesday.
Meanwhile, writing in The Sunday Times today, UK Brexit secretary David Davis says: "We don't want the EU to fail; we want it to prosper politically and economically, and we need to persuade our allies that a strong new partnership with the UK will help the EU to do that."
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