The 25-year-old is set to leave Turin this summer and would be available for €25m.
Goal says the Reds would like to sign the Brazilian.
However, Inter Milan remain favourites to secure his signature.
Any move from Liverpool would be predicated on the departure of fringe players.
Jurgen Klopp already has four centre-backs competing for two places.
Juventus are also interested in Bremer.
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