AS says Real see Rodri as a readymade replacement for Toni Kroos, who will hang up the boots after the summer's Euros with Germany.
Rodri, 27, is the big dream of Real president Florentino Prez.
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However, City are unlikely to let go of their key player, especially as he is under contract until 2027.
Bayern Munich's Joshua Kimmich, 29, is also on Real Madrid's wish list.