The Times says Manchester United are also keen on the Uruguayan and now face competition from Jurgen Klopp's side this summer.
Liverpool hold a concrete interest in Nunez but 'not at any cost'. He is understood to valued at around £68m and be leaning towards teams playing Champions League football.
The 22-year-old is widely expected to leave Benfica when the transfer window opens and the Portuguese side will hope to spark a bidding war for his signature.
Nunez has been one of Europe's breakout stars of this season, scoring an astonishing 34 goals in 40 appearances.
Liverpool understand there is value to be found in Portugal having signed Luis Diaz from Porto in January.
Source: Tribalfootball
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