Political gossip site Guido Fawkes listed Johnson and 11 Conservative Party MPs on Monday as quarantining on the instructions of the government's National Health Service (NHS) Test and Trace system.
Johnson entered self-isolation on Sunday after being contacted by Test and Trace to say he had come into contact with a person who had tested positive. Media speculation fixed on Ashfield MP Lee Anderson - who was among those named in the Guido Fawkes report - as the infected individual.
Meanwhile, The Times reported that Parliamentary authorities were discussing allowing Johnson to attend Prime Minister's Questions at noon on Friday via Zoom, an unprecedented move.
Johnson released a video via social media earlier on Monday, saying although he was "as fit as a butcher's dog" and "bursting with antibodies" following his bout of the virus in April, he would stick to the rules on self-isolation.