Off contract in June, Konate has so far resisted Liverpool's attempts to open talks about a new deal.
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Real Madrid, PSG and Bayern Munich have all expressed interest in taking Konate in a Bosman transfer next summer.
And L'Interista is reporting Inter are also interested in the France international.
A Bosman move is being discussed internally at the Nerazzurri, though a cut-price January attempt also hasn't been ruled out.