The Prime Minister defended the faltering flagship policy as arrived in Rwands, where he will also meet Charles for a discussion over cups of tea.
The heir to the throne is said to have added to wide-spread criticism of the project disrupted by legal problems by describing it as “appalling” in private remarks.
The PM could also lose two crucial by-elections.
Mr Johnson will on Thursday join the prince in the Rwandan capital where they are attending the Commonwealth Heads of Government Meeting (Chogm).
But the Prime Minister is planning to avoid visiting the accommodation in Kigali where migrants who arrive by unauthorised means would be deported to.
It is understood the Prime Minister will visit Charles for a cup of tea on Friday morning, but Mr Johnson is not eager to raise the policy of removing migrants who arrive by unauthorised means on a one-way ticket.
The meeting between Mr Johnson and the prince will be the first time they have spoken since the service for the Queen’s Platinum Jubilee and comes after the “appalling” remark was reported.
Speaking to reporters as he prepared to fly to Kigali, Mr Johnson said the trip is an opportunity “for us all to understand for ourselves what that partnership has to offer”.
“Let’s hope perhaps help others to shed some of their condescending attitudes to Rwanda and how that partnership might work,” he added.
Asked if he will tell the prince he is wrong, Mr Johnson said: “I have no evidence for the assertion you’ve just made about the prince’s comments. I can’t confirm that.
“What I can say is that the policy is sensible, measured and a plan to deal with the grotesque abuse of innocent people crossing the Channel.”
Also voters will go to the polls in by-elections in Wakefield and in Tiverton and Honiton, both triggered after the previous Conservative MPs resigned in disgrace.
The polls are seen as a key test for Boris Johnson’s leadership two weeks after 148 of his own MPs voted in favour of his removal in a confidence vote.
In Wakefield, a former industrial area in West Yorkshire, ex-Conservative MP Imran Ahmad Khan stood down after being found guilty of sexually assaulting a 15-year-old boy and jailed for 18 months.
Wakefield was one of the so-called Red Wall seats won by the Tories in the 2019 general election after being a Labour stronghold since the 1930s, but Labour is now hoping to take it back.
In Devon’s Tiverton and Honiton, Neil Parish, the Tory MP since 2010, resigned after admitting he had watched pornography on his phone in the House of Commons.
The Liberal Democrats are the main challenger in this rural south-western constituency, where they are hoping to recreate by-election wins in North Shropshire in December and Chesham and Amersham a year ago.
Victory for the Lib Dems would require overturning a Conservative majority of 24,239, but party leader Sir Ed Davey was confident they were “neck and neck” with the Tories on the eve of the vote.
Losing the Tory stronghold would be seen as a sign of Mr Johnson’s diminishing electoral appeal after partygate and amid the cost-of-living crisis, and could spark a further backlash against his authority.
The Tories face a steeper challenge in retaining the Wakefield seat, with Labour now odds-on favourites to overturn the 2019 Conservative majority of 3,358.
Tory candidate Nadeem Ahmed raised eyebrows by arguing last week that voters should still trust the party after Mr Khan’s sexual assault conviction, just as they still trust GPs despite the crimes of mass murderer Harold Shipman.