Theresa May is to reshuffle her cabinet on Monday, with a number of new faces expected to join her top team.
No 10 has described reports Education Secretary Justine Greening and Health Secretary Jeremy Hunt will be among those moved as “all guesswork”.
Philip Hammond, Boris Johnson, Amber Rudd and David Davis are among key figures expected to stay in place.
Labour said Mrs May should focus on the pressures in the NHS rather than what it said was a “desperate PR exercise”.
Other current ministers reported to be vulnerable include Leader of the House of Commons Andrea Leadsom, Business Secretary Greg Clark and party chairman Patrick McLoughlin.
The reshuffle, which will continue into Tuesday, is being seen as an opportunity for Mrs May to promote more women, with female ministers only currently making up six of the 23 full members of her top team.
She is also under pressure to preserve the balance between Brexit sceptics and enthusiasts, while showing the government has a purpose beyond leaving the EU, which critics say is monopolising ministers’ time.
The changes, which will be Mrs May’s third reshuffle since becoming PM in July 2016, were triggered by her sacking of Damian Green last month as first secretary of state.
BBC political editor Laura Kuenssberg says whilst prime ministers do not have as much power to shape their fortunes as the position suggests, Mrs May can at least choose the timing of this “big set piece moment in politics”.
By BBC political correspondent Susana Mendonca
There’s long been talk of a cabinet reshuffle and now Mrs May is finally going through with it – albeit she has been pushed into it because she had to sack her second-in-command Damian Green over porn allegations – which has left a gap at the top table.
The fact that she’s having an actual reshuffle could be seen as a sign that Mrs May is more emboldened now than she was after her party’s dismal performance in the general election, when she had no real choice but to soldier on.
But if, as the speculation suggests, only a few middle-ranking ministers get moved about and the big beasts like Chancellor Phillip Hammond and Foreign Secretary Boris Johnson stay put, it brings into question just how much strength Mrs May really has to shake things up.
There are those in the Conservative Party who want to see new talent rising up the ranks, so expect to see a nod to that.
But the danger for a prime minister with a tiny majority is that for everyone she promotes, another disgruntled potential enemy hits the backbenches, and Theresa May doesn’t need any more rebels.
Mr Green was fired from his position, a role in which he was effectively Mrs May’s deputy, in December after making “misleading statements” to the press about pornography found on his office computer in 2008.
There has been speculation Mr Hunt could be promoted to take on the role – which would see him deputise for Mrs May at Prime Minister’s Questions and chair a host of influential cabinet sub-committees on Brexit.
Mr Hunt, who has been health secretary for more than five years, was a remain supporter during the referendum but has been critical of the EU’s approach to the negotiations since then and has said warnings about the economic damage of leaving the EU have so far been over-stated.
Labour said if she promoted Mr Hunt, Mrs May would be “betraying” patients at a time when the NHS was going through one of the worst winter crises in its recent history.
“The prime minister is clearly detached from reality if she thinks the NHS was properly prepared for this winter,” Labour MP Andrew Gwynne said on Sunday.
“The prime minister should be singularly focussed on addressing this problem, and not engaging in a reshuffle that is little more than a desperate PR exercise.”
Alternatively, Mrs May could choose to dispense with the title of first secretary – which has not always been filled by some prime ministers – and instead simply appoint someone to the lower-ranked job of Cabinet Office minister which Mr Green also held.
Speaking on Sunday, the PM told the BBC’s Andrew Marr she would be making changes imminently but would not respond to speculation about how far-reaching they would be.
She had reportedly planned a sweeping overhaul of her cabinet before June’s snap election but after failing to win the election outright she ended up only making a number of modest changes.
This led to accusations of political weakness and claims from opponents that she was only continuing in the job at the behest of senior figures around her.
In the past two months, as well as losing Mr Green, the PM has also seen defence secretary Sir Michael Fallon quit amid allegations around his conduct and Priti Patel resign as international development secretary after a row over unauthorised meetings with Israeli officials. Both have since been replaced.