The news will be a big disappointment for some Tory MPs who were hoping he would join them on the campaign trail.
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No10 and Boris aides had suggested the men would team up in an election.
But the former prime minister had trips already in the diary before Mr Sunak called the General Election for July 4th.
Friends said they include professional speaking engagements and personal holidays.
Tory MPs have been privately writing to Mr Johnson begging for his help in the campaign.
Mr Johnson has recorded a video of support for the Tory candidate running in the seat of his close ally Nigel Adams.
He said: “It’s Boris Johnson here and I am urging you to vote for Charles Richardson as your Conservative candidate for Selby.
“He’s a fantastic candidate because he is a local man and he knows Selby.”
One Boris loyalist has even publicly called on Mr Sunak to let him stand as an MP.
Tory MP Andrea Jenkyns posted on X: “With so many MPs retiring, I think Boris Johnson should stand in one of those seats. We need him.”