Dominic Cummings claims Boris Johnson plans to quit after next election to "make money and have fun".
No 10 said the claim was "utter nonsense."
The former top aide released a cache of messages between himself, the PM, Health Secretary Matt Hancock and top officials which he says illustrate the chaos at the top of government at crucial stages in the pandemic response.
Mr Cummings said he was doing so now because waiting for the official public inquiry - which won't get underway until next year - will be too late.
He wrote: "The public inquiry cannot fix this. It will not start for years and it is designed to punt the tricky parts until after this PM has gone — unlike other PMs, this one has a clear plan to leave at the latest a couple of years after the next election, he wants to make money and have fun not ‘go on and on’.
"So we either live with chronic dysfunction for another ~5 years or some force intervenes."
Mr Cummings also took aim at Mr Johnson's leadership style, saying he would duck out of meetings "as soon as they got a bit embarrassing.
He said: "(the PM) does the whole ''let’s take it offline'' shtick before shouting ''forward to victory'', doing a thumbs-up and pegging it out of the room before anybody can disagree'?"
Mr Johnson's press secretary said: "The PM has been asked this before and has said himself it is "utter nonsense", and that still stands.
"As you know the PM was elected in 2019 and continues to focus on delivering on the manifesto we were elected on and leading the country out of the pandemic."
In the messages, Mr Johnson branded Matt Hancock 'hopeless' and said he should be replaced with Michael Gove as Covid gripped Britain last March.
He accused Mr Hancock and No10 of trying to "rewrite history" over the Health Secretary's actions during critical early moments during the pandemic.
And he accused Mr Hancock of "neglecting care homes and testing" throughout April, because he was "trying to focus effort on his press conference at the end of April claiming success" for his 100,000 tests a day target.
But the message dump did not include evidence that Mr Hancock had promised colleagues that all patients released into care homes would be tested first - something Mr Cummings had said he could and would prove.
Number 10 did not deny that the messages are genuine, but refused to answer questions about their content.
