Jeremy Hunt has said he is "seriously considering" running to replace David Cameron and leader of the Conservative Party and prime minister.
The health secretary, who has spent much of his time since the election battling strikes by junior doctors, said today there could be a second referendum on the terms of the UK's exit from the EU.
Hunt had previously said being health secretary would be he "last big job in politics".
However asked about a leadership bid on ITV's Good Morning Britain today, he said: "I'm seriously considering it, nominations close on Thursday lunch time, but want I want to do now is start making an argument as to what we do next as a country."
He later told Sky News: "We will find out in the next 48 hours because the nominations close on Thursday lunchtime."
If he stands, Hunt is likely to face a crowded field of other candidates including Boris Johnson, Theresa May, Stephen Crabb and Nicky Morgan.
This morning George Osborne ruled himself out of running for the leadership in the wake of the Brexit vote.
But he said there was no reason the next Tory leader could not be someone from the 'Remain' campaign - such as Hunt, Crabb, May or Morgan.
"I’m not backing any candidate at the moment, but of course I was full-throttled in arguing for remaining in the EU, and because half my party wanted to leave the EU I don’t think I can be the person who can bring the party together at this moment. I’m just being realistic about that," he said.
But Osborne hinted he was keen to stay on in the cabinet under a new prime minister.
"That is absolutely a decision or the next Prime Minister, not for me. I will do whatever I can to help my country at this moment of need," he told BBC Radio 4's Today programme.