The Prime Minister has opened the door to a potential reshuffle later this month as part of a bid to ensure that she has "the best people in my Cabinet".
As well as promoting a new generation of Tory MPs, Mrs. May has signaled that she is willing to replace ministers who have shown disloyalty, The Telegraph reported.
Asked what she might do with the Foreign Secretary in a reshuffle, she told The Sunday Times: "It has never been my style to hide from a challenge and I'm not going to start now.
"I'm the PM, and part of my job is to make sure I always have the best people in my cabinet, to make the most of the wealth of talent available to me in the party."
Her comments will be viewed as a slapdown to Mr. Johnson, whose activities overshadowed much of the Tory conference until Mrs. May's ill-fated speech. Although to muddy the waters further, the Foreign Secretary issued a plea for warring party members to unite behind the Prime Minister in this morning's Sunday Telegraph.
Elsewhere Sir John Major lashed out at "disloyal" Tory MPs and ministers as he urged them to back Theresa May - but suggested she must take radical action to win over voters by increasing public spending and reviewing controversial welfare changes.
The ex-Tory leader, whose own premiership was marred by infighting and plotting, said he had viewed the turmoil in the Conservative Party with "increasing dismay".
But alongside his appeal for unity, Sir John called for radical action on Mrs. May's social justice agenda to "win back hearts and minds" or risk the prospect of "neo-Marxist" Jeremy Corbyn taking the keys to Number 10.
Ruth Davidson said there had been some "unfortunate shenanigans" in the party "but the pushback has been pretty strong" against those trying to force a leadership contest.
The Scottish Tory leader hit out at colleagues engaged in "tittle-tattle", adding that being a politician is "about delivering for the country, it's not and should never be about private ambition" - comments likely to be viewed as a swipe at Mr. Johnson.
Ms. Davidson told BBC One's Andrew Marr Show the Foreign Secretary had backed Mrs. May's Florence speech on Brexit and she should "hold him to that".
"He is a big intellect, a big figure in the party and if the Prime Minister believes he is the right person to be Foreign Secretary then she has my full support," she said.