A story published by the Daily Mail on Monday claimed the prime minister made the comment during a meeting in No.10 in October. The paper did not give a source for the allegation.
But it comes after Dominic Cummings, Johnson’s former top adviser, launched an extraordinary public attack on his former boss.
Speaking to Sky News, Wallace said of the allegation: “Look, it is not true, it has been categorically denied by practically everyone.
“We are getting into the sort of comedy chapter now of these gossip stories — unnamed sources, by unnamed advisers talking about unnamed events.
He added: “All the ‘who said, what said’, I’ll leave that to the Oscar gossip columns that are now being rolled out today after last night.
“I’ll leave that to the Hello magazines of the world but government is focused on delivering for the citizens on its Covid response.”
The Daily Mail reported Johnson said: “No more ****ing lockdowns – let the bodies pile high in their thousands.”
The UK’s most senior civil servant is expected to indicate later on Monday he has not cleared Cummings over the so-called “chatty rat” leak of plans for a second lockdown.
Simon Case, the cabinet secretary, is expected to say his inquiry into the leak last autumn is still “live” when he appears before the Commons public administration and constitutional affairs committee (PACAC).
In a blog post on Friday, Cummings accused Johnson of seeking to block the investigation after learning that a close friend of his fiancee Carrie Symonds had been implicated, a claim the prime minister denied.
“It is sad to see the PM and his office fall so far below the standards of competence and integrity the country deserves,” Cummings said.
Labour is also demanding answers on another of Cummings’ allegations as it attempts to force ministers to explain how Johnson paid for the lavish refurbishment of his official Downing Street flat.
The opposition will ask Commons Speaker Lindsay Hoyle to grant an urgent question requiring a minister to come to parliament to respond to the charge that Johnson plotted for Tory donors to secretly fund the work.
Over the weekend, the international trade Secretary Liz Truss insisted Johnson had complied fully with the rules and had paid for the refurbishment, which reportedly ran to £200,000, out of his own pocket.
But during a round of broadcast interviews, she repeatedly refused to say whether the bill was initially settled by the Conservative Party, or one of its donors, in which case it should have been declared as a loan under party funding rules.