Bayern had a €65m offer rejected by Liverpool at the beginning of the week, with the Reds insisting Diaz won't leave for less than €100m.
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However, Diaz has informed Liverpool he'd like them consider Bayern's offer as he weighs up whether now is the time to leave Anfield.
BILD says Bayern are ready to try again and are pushing Liverpool to compromise on their valuation.
Indeed, it's also reported Diaz has now agreed contract terms with Bayern in a clear indication he's eager to leave this summer.