Mr Johnson acknowledged that taxpayers would baulk at the cost of buying a jet for ministers, but said he thought the spending would be justified if it was not "exorbitant".
He complained the RAF Voyager jet which is shared by the Prime Minister, senior Cabinet members and the Royal Family "never seems to be available".
And he suggested its impact as a travelling symbol of Britain is undermined by its drab grey colours.
He had to stop off in Madrid to change planes on his Air Europa service from London to Lima, adding five hours to the journey time, because the only direct flight on offer did not fit his schedule.
But he insisted it was not his own comfort he was concerned about, using an arcane term for staying overnight as he joked: "We are hard as nails, we Foreign Office types. We don't care about changing planes, we pernoctate on planes."
Asked if he would like to have a "Brexit plane", he told reporters: "If there's a way of doing it that is not exorbitantly expensive then yes I think we probably do need something.
"The taxpayers won't want us to have some luxurious new plane, but I certainly think it's striking that we don't seem to have access to such a thing at the moment."
The Foreign Office currently has use of the Queen's Flight fleet of BAE 146 jets, one of which Mr Johnson used to fly to Moscow before Christmas.
He described the 26-seater planes as "superb... masterpieces of engineering", but said they were coming up to 40 years old.
Tony Blair's plans for a prime ministerial jet - branded "Blair Force One" for its similarity to the US President's private airliner - were dumped by Gordon Brown as a cost saving measure.
The Voyager began its work transporting VIPs in 2016, after a £10 million refit under David Cameron.
But he took only one flight on it before handing over to Theresa May, whose travels have earned it the nickname of the "ThereasyJet".
Mr Johnson revealed its multiple users mean it is difficult for senior ministers to book when they need it, saying: "What I will say about the Voyager, I think it's great, but it seems to be very difficult to get hold of.
"It never seems to be available. I don't know who uses it, but it never seems to be available."
And he added: "Also, why does it have to be grey?"
Mr Johnson has been a prominent supporter of the campaign for a replacement for the Royal Yacht Britannia.
It is thought a Brexit plane could play a similar role in projecting UK "soft power" around the world.