The prime minister could storm out of talks over Britain’s divorce bill, which could be as much as 100 billion euros (£87.7 billion), it is believed.
Senior members of the Government have previously argued that Britain should not have to pay up, amid suggestions that added EU demands could send the bill soaring.
According to The Sunday Telegraph, a senior Downing Street figure briefed business leaders and City bosses after last month’s General Election.
A source told the newspaper: ‘I do think we are looking to be as hard-nosed, as hard-headed and as cold-eyed about this as it is possible to be.
‘If any of those actions take place it will be to work towards a single objective – getting the best deal that we can.’
While no final decision about Mrs May’s negotiation tactics has been made, there is a distinct possibility she could quit talks, the source said.
A Downing Street source told the newspaper: ‘This suggestion has no part in our plans.’
Financial markets are expected to suffer if talks between Britain and the EU go badly later this year.
The EU has said Britain will have to ‘clear its accounts’ as it prepares to leave the bloc, but it is unclear how much would be demanded and what the Government expects to pay.