The banner, organised by the campaign group RodgersOutClub, read "Rodgers Out, Rafa In."
Rodgers is the first Liverpool manager in over 50 years to not win a trophy in his first three seasons at the club but last season guided the club to the brink of a first Premier League title.
"About to leave for Anfield. Hope this Rodgers banner supposedly flying over the ground is called off as it's embarrassing to club and fans," former Reds defender Jamie Carragher tweeted earlier on Saturday.
Rodgers has reiterated on a number of occasions that he is the right manager for Liverpool and said he had the backing of the club's American owners, Fenway Sports Group.
Former Liverpool manager Rafa Benitez, who led the club to Champions League success in 2005, is currently the manager of Italian side Napoli.
(Reporting By Tom Hayward, editing by Pritha Sarkar)
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