Pressure has been building up on May to step down after a disastrous election result for the Tories, which saw the ruling party's majority slashed and being forced to cobble together a minority government with the support of Northern Ireland's Democratic Unionist Party (DUP).
"A handful of senior people have pledged their loyalty to Boris at Cabinet level," a Johnson ally told 'The Sunday Times'.
But Johnson reacted to media speculation on Twitter by dismissing any rebellion: "I am backing Theresa May. Let's get on with the job."
The latest leadership speculation comes a day after two of May's closest advisers, her joint chiefs-of-staff Fiona Hill and Nick Timothy, resigned amid recriminations about their controlling management style.
May had been reportedly given an ultimatum to get rid of the duo or face a leadership challenge by Monday.
The new editor of the 'Evening Standard' newspaper and close ally of Cameron added: "Cameron took years getting back to office, winning in seats like Bath and Brighton and Oxford and I am angry when we go backwards and I am not afraid to say that."
The sense of uncertainty about a May-led minority government was made worse on Saturday night by conflicting messages from Downing Street.
"The Prime Minister has tonight spoken with the DUP to discuss finalising a confidence and supply deal when Parliament returns next week. We will welcome any such deal being agreed, as it will provide the stability and certainty the whole country requires as we embark on Brexit and beyond," the final statement said.
Meanwhile, DUP leader Arlene Foster has said that talks were ongoing, indicating it may not be such a smooth process after all.
The Opposition Labour leader, Jeremy Corbyn, has also said that his party is waiting in the wings to take charge after he defied pollsters' predictions by gaining 30 seats in Thursday's election, leaving a hung Parliament.
"We can't go on with a period of great instability," he said, adding that the Labour Party was ready to fight another election campaign.
A latest YouGov poll for 'The Sunday Times' revealed that voters, by a margin of 48 per cent to 38 per cent, believe the Prime Minister should resign and for the first time Corbyn has drawn level with May on the question of who would be the best Prime Minister.
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