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The French international centre-back, who's been linked to Real Madrid, is now in the final year of his contract at Anfield, and there are no signs of him signing a new deal on Merseyside.
Negotiations with Liverpool have hit a stalemate in recent months, and it's believed that Real Madrid are considering snapping up Konate on a free transfer after recently securing Trent Alexander-Arnold from Arne Slot's champions.
However, it's understood that an undisclosed club from Saudi Arabia reached out to Konate through his representatives last week, expressing interest in signing the former RB Leipzig stalwart this summer.
But Konate declined the opportunity to enter negotiations, reaffirming his commitment to remain in Europe, where he wishes to continue playing at the top level.
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Had Konate shown any interest in the move, the unnamed suitor would have been prepared to initiate talks with Liverpool regarding a potential deal.
Liverpool is keen to settle Konate's ongoing contract issue, but there's a growing feeling that the 26-year-old might be holding out for a move to Real Madrid
Whether Liverpool would entertain offers for Konate this summer, given his contract situation is currently uncertain, remains to be seen as no formal proposals have been received yet.
For now, the champions seem to be focusing on securing a high-profile attacker, having expressed interest in Newcastle's star player Alexander Isak.
Newcastle is reluctant to let go of its talisman, but Liverpool is also considering Eintracht Frankfurt striker Hugo Ekitike if negotiations with Newcastle fall through.
Eddie Howe's team has already had a bid of up to $92M including add-ons turned down for the Frenchman, whom they'd like to pair with Isak at St James' Park.
Meanwhile, Liverpool have dismissed an initial offer of up to $79M from Bayern Munich for Luis Diaz.
The Colombian international is reportedly open to a move, but Liverpool is keen to retain him and believes Bayern's offer falls short of his market value.
Napoli have also shown interest in Darwin Nunez, who has attracted fresh attention from the Middle East, but so far, the Italians haven't met Liverpool's asking price.
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