A Daily Mail report alleged that the prime minister said at an October meeting at Downing Street: “No more f****** lockdowns - let the bodies pile high in their thousands.”
However, Mr Wallace “categorically denied” the allegations.
“It’s not true - it’s been categorically denied by practically everyone,” he told Sky News on Monday.
“We’re getting into the sort of comedy chapter now of these gossip stories - you know unnamed sources by unnamed advisers talking about unnamed events. You know - look - none of this is serious.”
The Cabinet minister told BBC Breakfast the claims were "ludicrous".
"I've known the Prime Minister for many years, that is not the Prime Minister I know - that is just nonsense," he said.
"He has denied it, No 10 have denied it.
"Where we are at right now is unnamed people talking about unnamed conversations with different people and that isn't really solid journalism."
Health minister Nadine Dorries also dismissed the claims.
She tweeted: "This is an outright lie. Not one named source or substantiated fact.
"Days before Hartlepool by election and a wide set of local/PCC/Mayoral elections.
"It’s mendacious, vexatious co ordinated gossip given in order to negatively influence the outcome," she claimed.
Allies of the prime minister’s former adviser stated that he had documents from his time in No 10 that he could use in evidence when he appears before MPs on May 26.
One of the most damaging claims to Mr Johnson is that he allegedly refused to back a ‘circuit-breaker’ lockdown last September, despite evidence showing that a mounting rise in infections would be the result.
According to the Times, Mr Cummings is preparing to expose private statements made by Mr Johnson that shows he was prioritising keeping the economy open over a rise in Covid-19 related deaths.
An ally of Mr Cummings told the paper: “He’s going to be forensic. He’s going to say things that are verifiable, that are backed up by documents and emails.”
Another said that Mr Cummings had “boxes and boxes” of documents from his time in Downing Street.
“Boris is just making it more likely that Dom’s evidence will be more forthright than it otherwise would have been,” one of his allies said.
Mr Cummings launched an attack on his former boss via his blog on Friday, including claims that Mr Johnson had attempted to secure funding from Conservative supporters for renovations for his Downing Street flat.
Trade Secretary Liz Truss also backed up claims that Mr Johnson covered the renovation costs, telling the BBC’s Andrew Marr Show on Sunday that it was "from his own pocket".
However, she did not answer repeated questions on whether a Tory party donor initially provided the money to him.