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ESPN are reporting this and say the 21-year-old Frenchman would cost around £32m to sign from Sevilla, having only joined from Bordeaux for €27.5m last summer.
Kounde made 29 La Liga appearances in the 2019/20 season, helping Sevilla secure Champions League qualification.
Zinedine Zidane is reportedly keen to have more options for the upcoming window with Real in the market for another defender.
Eder Militao joined Real last summer but has failed to impress, making just 15 appearances since his €50m move from Porto, while Sergio Ramos, 34, is in the latter stages of his career.
Florentino Perez, president of Real Madrid, has declared that "this summer there will be no great signings. Real Madrid will return to sign the best when the situation changes".
No media in Spain has echoed Real tracking Kounde.
Sergio Ramos is about to renew and with Raphael Varane, Militao and Nacho or Ferland Mendy, who has already played at centre-back, the position is covered.
Real Madrid monitor around 100 players each season. Kounde could be one of them, but there has been no movement or concrete interest in signing him so far. At the moment it is only a rumour.
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