According to The Times, demotions could be announced as soon as Thursday and would include Foreign Secretary Dominic Raab, Home Secretary Priti Patel, and Education Secretary Gavin Williamson.
Johnson repeatedly dodged questions about any purported cabinet reshuffle at a press conference on Tuesday evening.
He dealt with further questioning on Wednesday during Prime Minister's Question (PMQs) time in the British Parliament.
During the PMQs, Labour MP Peter Kyle questioned the PM's confidence in Education Secretary Gavin Williamson.
"With a net approval rating among Tory supporters of -53, can the prime minister get to his feet, put hand on his heart and promise the country, this House and his own supporters that the education secretary is the right person for the job and he is up to the job?", Kyle asked.
Johnson responded by saying that Williamson "has done a heroic job of dealing with very difficult circumstances in which we had to close schools during the pandemic".
The competence of the cabinet members has also received the attention of online commentators.
Williamson's aides on Wednesday revealed that the education secretary mistook a rugby player, Maro Itoje, for English footballer Marcus Rashford during a Zoom meeting.
Manchester United footballer Rashford successfully campaigned in 2020 to end child hunger in the UK by providing free school meal voucher systems for low-income children.
Both Raab and Williamson have seen a drop in their ratings in the Cabinet approval league table, run by the website Conservative Home.
Downing Street earlier said there were "no plans for any reshuffle".