The Reds have moved for the Brazil international after having a €120m offer for Alexander Isak rejected by Newcastle last week.
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ESPN Brasil says Liverpool are now set to discuss a fee with Real Madrid after reaching contract terms with Rodrygo.
Journalist Siro Lopez is reporting: "Liverpool have spoken to the entourage of Rodrygo, and the Real Madrid forward has approved an informal offer of personal terms."
A first formal offer from Liverpool is now set to be tabled.
Rodrygo is also a summer target for Arsenal and Tottenham.