Southampton signed Mane in 2014 for just £11.8m - turning in a £22m profit in just two seasons.
Express Sport understand Mane will be Liverpool's big summer signing, with their midfield target being Piotr Zielinski, who has played just once for Poland at Euro 2016 and did not feature in 120 minutes against Switzerland on Saturday before the tie was settled in his country's favour on penalties.
Liverpool's initial reluctance to pay £10m for Leicester's teenage left-back Ben Chilwell has seen Hull City's Andrew Robertson discussed.
Southampton and England left-back Ryan Bertrand has one year remaining on his contract.
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