The Daily Mirror say Atletico Madrid’s 20-year-old Lucas Hernandez is being monitored along with Leicester left-back Ben Chilwell, 19, and Fulham full-back Ryan Sessegnon, 15.
Arsenal are set for an active transfer window with doubts over several players, including Per Mertesacker and Kieran Gibbs.
Liverpool v Villarreal - Europa League match preview
Zielinski, on season-long loan at Empoli from Udinese, recently admitted he held talks with Klopp.
And La Gazzetta dello Sport reporter Nicolo Schira revealed on social media: "Liverpool wants to close Piotr Zielinski. Klopp has offered [£12m] to Udinese for him."
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