The pair will visit Belfast on Tuesday where they are likely to be grilled on their proposals to resolve the Irish border issue and remove the controversial backstop.
Mr Hunt has said he believes there is “technology there now” to provide a solution, while Mr Johnson has suggested the backstop issue could be solved during the implementation period.
The hustings come after Mr Hunt told Sky News that German Chancellor Angela Merkel is willing to look at new Brexit proposals put forward by the next prime minister.
He said: “I’ve had a conversation with Angela Merkel and… (she said) ‘of course we will look at any proposals made by a new UK prime minister’, because she wants to solve this problem.
“And providing we’re sensible, and I think the approach that I’ve laid out is a sensible approach and a fair approach, and I think that it’s in Germany’s interests as well.
“What she has said is she will look at the package and I think she will look at it with an open mind.”
Mr Johnson, who rejected an invitation to take part in the interview, told party members during a “telephone town hall” event on Monday evening that he was the “right guy now to deliver for our party”.
“We need someone who believes in Brexit and can deliver it,” he said.
Mr Hunt and Mr Johnson are likely to face questions on the investigation of Northern Ireland military veterans, as well as their spending pledges.
Over the weekend they both backed calls for increased legal protection for UK troops and veterans.
Elsewhere, the Daily Telegraph reported that allies of Mr Johnson are urging him to shrink the size of the Cabinet by merging Government departments.
However a campaign source told PA: “This is absolute nonsense.”
Work and Pensions Secretary Amber Rudd, who is supporting Mr Hunt, rebutted the suggestion, tweeting: “Fold DWP? We’re a delivery Department giving tailored support to people trying to get into work, with brilliant work coaches at 600+ sites.
“80,000 staff and £100bn in pension payments across the world. Can’t imagine @BorisJohnson supports this unworkable ‘plan’ by “allies”.”
Tory former de facto deputy prime minister Damian Green, a backer of Mr Johnson’s campaign, dismissed the report, telling BBC Two’s Newsnight: “I just find that quite an extraordinary proposition.”
Meanwhile Hilary Benn, Labour chairman of the Exiting The European Union Committee, insisted it was still possible to stop the UK crashing out of the EU, despite an attempt to shut down Government spending in the event of a no-deal Brexit appearing to have stalled.
He told Newsnight: “When you get to the moment when Parliament is actually looking at this, then I believe the House of Commons will act, because I am still of the view that there is not a majority in Parliament for a no-deal Brexit.”