The 26-year-old will enter the final season of his contract at Liverpool in 2025-26 and talks over a new deal are understood to be slow.
Now, according to a report from Spanish outlet Marca, Konate has told the Premier League champions he would like to join Real Madrid this summer, but only if they come in for him.
Xabi Alonso’s side are interested in bringing in a new centre-back, despite the signing of Dean Huijsen, and have the big Frenchman on their shortlist.
Real Madrid are more likely to make a move in the new year, once Konate is able to negotiate with foreign clubs, should he not sign a new deal with Liverpool in the near future.
Of course, they pulled off the same trick with Trent Alexander-Arnold this summer, something Liverpool will undoubtedly want to avoid happening again.