A banner saying 'Rodgers Out, Rafa In' was flown over Anfield ahead of Liverpool's Premier League match with QPR.
A group claiming to be Liverpool fans earlier on Saturday tweeted a photograph showing the banner, which appeared to be laid out at an aircraft hanger.
The organisers call themselves the @RodgersOutClub.
They tweeted: "We are a group of lifelong Liverpool fans who have had enough of Brendan Rodgers. We will not be silenced or ignored until he is gone. Fact."
They are also demanding the return of former boss Rafa Benitez - who often punctuated his press conferences with the word 'fact'.
The protest may be the first real signs of discontent amongst supporters since Rodgers arrived at the club, although some posts on social media have also suggested it may be a stunt organised by rival fans.