Not quite in those naked promissory terms, but... Rees-Mogg (low hanging fruit, I know) said something more conditional after the Audi boss made some noise in mid 2018:
THE head of one of Germany’s biggest car makers has called for a tariff-free trade deal with Britain.
Audi chairman Rupert Stadler said he wanted the EU to find a deal that would preserve existing markets on both sides of the Channel. Asked if he was concerned about the impact on UK sales — and the knock-on effect on German jobs — in the event of post-Brexit tariffs, he said: ‘We don’t want tariffs. I’m a big fan of fair trade and free trade.’
Mr Stadler said there would be no winners if the EU and the UK didn’t strike a deal.
Eurosceptic Jacob Rees-Mogg welcomed the comments and said it suggested EU chief negotiator Michel Barnier was out of step with the interests of member states. The Tory MP said it was also important because German leader Angela Merkel ‘has a good track record of backing Germany’s industrial interests’. He added: ‘The unity of the EU is fraying — the question is whether things will move in time.’
Random fact: Stadler was arrested soon thereafter in the emissions probe.
Stadler was not the only guy on the German side to "break ranks"; e.g., this year:
The boss of the IFO Institute [Gabriel Felbermayr] said steps should be taken to keep the "EU and the UK in a joint customs territory after 2020". [...]
While German business groups were maintaining a tough stance to avoid undermining the European Commission's negotiating stance, Mr Felbermayr said the EU should take a softer approach.
"The EU should, as a quick fix at least, offer to remove both the backstop and the withdrawal agreement's current time limit on the mobility of goods and capital so that the provisional agreement would keep the EU and the UK in a joint customs territory association even after 2020 without making a difference between Northern Ireland and the UK. That would be key," he said.
I'm sure some Brexiteers have picked up on this as well, I can't be bothered to search for their reactions.
And I'm not sure how this particular claim (of easy negotiations with the EU) is more relevant than other implausible ones regarding trade or the economic impact, e.g.
Liam Fox promises to sign 40 free trade deals the 'second after' Brexit [...]
The Secretary of State for International Trade insisted the UK would easily be able to copy and paste all 40 of the EU's external trade deals "the second after midnight" on Brexit day in March 2019.
"We're going to replicate the 40 EU free trade agreements that exist before we leave the European Union so we've got no disruption of trade," Fox told a Conservative party [...] event in Manchester.
"I hear people saying 'oh we won't have any [free trade agreements] before we leave'. Well believe me we'll have up to 40 ready for one second after midnight in March 2019," he told cheering Tory activists. [...]
Fox also dismissed claims that a no-deal Brexit would have a negative impact on the British economy. [...]
"People talk about this as if it's some sort of horror awaiting us," the Tory minister said.
"But that's how we conduct our business most of our time. The rest of the world trade on those [WTO] terms. It'd be better if we got a fully comprehensive deal but we don't need one."
And unlike Davis, Fox is still in the Cabinet.
Basically "no deal, no big deal" or "no deal, no problem". It seems to me this actually was and is a lot more common theme (see 1, 2, 3 etc.) in the hard Brexit camp. I'm not sure anyone tallied their promises that are a variation on that...
It doesn't came with a full transcript alas, but Boris Johnson said just this month
The top Brexiteer insisted Brussels will end up caving at "five minutes to midnight" after Theresa May's deal was defeated.
He told LBC: "The horses always change places in the final furlong and it's always at five minutes to midnight that the real deal is done, in Brussels the final fix is only done at the end.
"They will have to consider how to get a better arrangement with the UK." [...]
"Whatever happens there will be a deal, there will be an arrangement between the UK and the EU."
This is somewhere in-between "negotiation will take 10 minutes" and "no deal, no problem", but is basically still a promise the EU will cave in.