Kroos' future has been the subject of speculation for months, with Manchester United having been frequently linked with a move for the Bayern Munich midfielder.
Spanish giants Real are reported to have stolen a march on the Premier League club, though, and Kroos is said to be set to move to the Santiago Bernabeu when Germany's FIFA World Cup campaign finishes.
Former Germany captain Matthaus believes the 24-year-old will add a new dimension to Carlo Ancelotti's side if he completes his move to the La Liga club.
He told Marca: "Congratulations to Real Madrid, they've got themselves a genius there. All the same, I'd have preferred him to stay at Munich.
"Toni is very intelligent, he passes the ball brilliantly and he can shoot hard and well, too. (Cristiano) Ronaldo and (Gareth) Bale can really expand alongside him. (Arjen) Robben and (Franck) Ribery have, in the past few years.
"He isn't a central midfielder, he's more of a false (number) nine who should go through the middle, behind the forwards.
"I can imagine Cristiano Ronaldo, Kroos and Bale together in that line of three behind (Karim) Benzema. He is like (Luka) Modric in that way, though Modric can play as a central midfielder and Kroos is not one of those."
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