The 18-year-old Japan international is currently on loan at Real Mallorca after joining Los Blancos in the summer.
"He's a very good player," Kagawa told MARCA.
"He already speaks Spanish because he was at the Barcelona academy for a bit and this is helping him a lot now.
"I think he can play well for Real Madrid.
"He has a very good chance [of succeeding in Spain].
"He's left-footed and very intelligent on the pitch.
"He always makes the right decision at the right time."