The Hoops' top brass want the former England boss, 57, to succeed Ian Holloway at Loftus Road, says the Mirror.
McClaren has been out of work since parting company with Israeli outfit Maccabi Tel Aviv – where he had been employed as a coaching consultant – in December.
His last job in English football was a second spell at Derby where he was sacked in March 2017.
Holloway ended the Hoops' Championship season with a 2-0 defeat at Leeds and just three wins from the final nine games. The west London club finished 16th.