Rossi says his Hungary captain sees his future with Real Madrid.
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The Italian is quoted by Marca as saying: "Because of the very close and direct relationship I have with Dominik Szoboszlai since he started playing football as a child, Real Madrid has always been his dream.
"I don't know if he'll be able to take that step, because the decision depends on him and also on his club."
Indeed, Rossi also stated: "I absolutely don't rule out the possibility of him staying at Liverpool and renewing his contract there, especially because he's highly valued within the club."
Szoboszlai is under contract at Anfield until 2028.