Steve Baker previously insisted the prime minister would have to do a deal with Farage if there was an election before Britain leaves the EU or face “losing Brexit”.
Britain is heading for a December general election after Johnson broke his pledge to deliver Brexit “do or die” on October 31.
But Baker, whose European Research Group (ERG) MPs have swung behind Johnson’s withdrawal deal, said Farage’s demand for the Tories to pursue a no-deal Brexit “won’t happen”.
The former minister told HuffPost UK: “A pre-Brexit pact with the Brexit Party won’t happen all the time Nigel Farage insists the Conservatives pursue no deal, which won’t happen.
“Boris will have to win without any arrangement.”
Farage has criticised Johnson’s deal, insisting it is “very disappointing for all Leavers” because it is “just not Brexit”.
And responding to Baker’s comments, the Brexit Party’s head of press Gawain Towler suggested the Tory MP would have opposed Johnson’s deal had his predecessor Theresa May proposed it.
Brexit Party chairman Richard Tice on Tuesday morning refused to guarantee it would stand candidates against the Tories, although he insisted Johnson’s deal is “full of flaws and pitfalls” and demanded the PM back a “clean break” (no-deal) Brexit.
Asked if the Brexit Party would definitely stand candidates against the Tories, he told BBC Radio 4’s Today programme: “Let’s wait and see.
“We will not negotiate live on air with your good self, we will negotiate with the Conservatives.”
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Tice also suggested that the Brexit Party could target Labour-backing Leave voters in areas that have not returned a Tory MP for decades.
“There’s over a hundred seats in this country that have not been Conservative for over a hundred years and all of those seats in the European election voted for the Brexit Party.
“So actually on this issue, on a clean break Brexit, we actually far from being frit, we’re actually extremely confident that actually that’s what Leave voters are very very prepared to vote for and we think they should be given that choice.”
Tice described Johnson’s deal as a “trap”, because it would leave the UK in a standstill transition period during which it would follow EU rules until the end of 2020, or until a trade deal is agreed if the government sought an extension.
“We don’t like this deal that he’s done, it’s full of flaws and pitfalls, and the more that people start to look into it... they will realise that actually this is another trap,” Tice said.
“The Theresa May deal we were trapped by the backstop, under this deal, we’re trapped by the transition which [EU chief Brexit negotiator] Michel Barnier a few days ago said would be at least three years.”
Tice added: “It is quite clear that a Leave alliance will deliver what this country needs, which is a thumping majority in order to get Brexit done.
“What we said to the Conservative party in September – Boris if you stand for a clean break Brexit, which is actually the right way, it’s the best thing for the country, then we will put country before party and we will stand down and not fight your candidates.
“That generous offer remains.”