Mr Farage said Mr Johnson should recognise that his party had a “lot better chance of winning a seat like Pontefract”, adding: “There is a possibility that an electoral pact could be forged.”
But Matt Hancock, tipped as a possible deputy prime minister when the new cabinet is announced over the next 24 hours, ridiculed the idea.
“There is no way we are going to have any kind of electoral pact with the Brexit party and with Nigel Farage,” the current health secretary insisted.
Mr Hancock insisted Mr Johnson’s priority would be to “deliver on Brexit and on the domestic agenda”, then defeat the Brexit party in an election “a long way off”.
“I don’t want to see an early election, Boris doesn’t want to see an early election,” he told BBC Radio 4’s Today programme.
“We are not going to have an electoral pact with any other party, we are going to defeat other parties.”
However, despite the denials, many observers believe Mr Johnson will have little option but to pursue a pact if the Brexit crisis triggers an election this autumn.
Many Tories fear disaster if they fight the Brexit Party while the UK remains in the EU, after it triumphed in May’s European elections with almost 32 per cent of the vote – with the Conservatives on just 9 per cent.
A snap election would be necessary if Mr Johnson sticks by his pledge to deliver Brexit by 31 October “deal or no deal” – having failed to negotiate a fresh deal and if MPs block a no-deal.
Mr Farage predicted an election was inevitable, saying of Mr Johnson: “He is going to have to risk his longed-for position as PM to ensure Brexit is enacted properly.
“There is no prospect of a meaningful Brexit thanks to the views of most sitting MPs. And any attempt to prorogue parliament will lead to the PM being brought down by his own side.”
Writing in The Daily Telegraph, he said an election would split the Tories, so “for this strategy to work, he will need the support of the Brexit Party”.
The comments come after Donald Trump, in unwelcome remarks for the Johnson camp, praised Mr Farage and said “he is going to work well with Boris”.
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