The Holland midfielder penned a new contract to 2032 on Saturday.
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The Times says Liverpool chiefs will now turn to several of Gravenberch's teammates.
Dominik Szoboszlai is already in talks with Liverpool about a pay-rise and extension.
Liverpool also are stepping up talks with Alexis Mac Allister's camp, while there remains hope of securing Ibrahima Konate to a new deal.
Konate's situation is the most complicated, with his current deal to expire at the end of June.
