Michael Gove has said he is "not wedded" to the idea of leaving the EU on October 31.
The environment secretary and Tory leadership contender said the UK should not be held to a fixed date in order to secure a Brexit deal.
But he told an event in London that any delay would be weeks, not months.
"The critical thing to do is recognise if we're not 100 per cent out by midnight on October 31, then we risk making that arbitrary deadline the determinant of what a good deal is," he said.
"If we're so close to the wire with what I believe is a better deal, it would be right to take those extra few days or weeks in order to land it and to make sure that we're out."
The October 31 deadline was set after Brexit day was pushed back to April 12, following the initial March 29 exit date.
Brexit has been a divisive issue for the eleven leadership contenders.
International development secretary Rory Stewart seized on comments by ex-Brexit secretary Dominic Raab that he could close down Parliament as PM to force through a no-dealBrexit, branding the move potentially "illegal".
Mr Stewart said: "All this talk about no-deal Brexit is a recipe for delay. It can't be done.
"And the the reason why Dom Raab is saying he is going to prorogue Parliament, in other words try to shut the doors on Parliament, is because the only way that they could try to get it through is by doing that.
"That would be illegal, if they did it for the express purpose of getting it through.