Boris Johnson has refused to answer questions over whether he will make changes to his Cabinet in the coming days.
Persistent speculation has suggested that the Prime Minister is preparing a wider reshuffle to clear out underperforming senior ministers.
Reports have suggested that Foreign Secretary Dominic Raab could be moved in response to his handling of the Afghanistan crisis.
Education Secretary Gavin Williamson has also been tipped to be at risk.
Both have seen a drop in their rating in the Cabinet approval league table run by website ConservativeHome.
But the Prime Minister would not be drawn on the rumours at a press conference on Tuesday to coincide with announcements on social care.
Mr Johnson was asked by multiple journalists whether he would be conducting a reshuffle, but on each occasion failed to respond to the question.
Closing the briefing, he said if he had avoided questions on “more political matters” it was “because this is a press conference that is focused on, I think, what matters to the people of this country, which is building back better from Covid, fixing the backlogs in our NHS and fixing social care at the same time.”
The Sunday Times reported that a reshuffle could take place this week to act as a distraction to the expected social care row.
Downing Street previously said there were “no plans for any reshuffle”.