Lucas Leiva is set to stay with Liverpool this season.
Inter Milan will not make an offer for Lucas after the asking price was set too high.
Inter are under the scrutiny of UEFA's Financial Fair Play authorities and cannot part with big money unless they see it as value for money.
Lucas was also a transfer target for Napoli, but bosses at Anfield have successfully fended off approaches and Rodgers last week insisted his man was staying put.