Sky Sports claims that the Reds have already made contact with the Serie A club while assessing a possible move for the former Everton wing player.
Arsenal would also be sharp, while clubs in the Saudi Pro League have shown interest for the 26-year-old.
Lookman is generally expected to leave Atalanta at the end of the season, where Liverpool sees him as a possible successor to Mohamed Salah.
The winger has been huge for the Italian Serie A club and recently helps them win the Europa League.
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