The 35-year-old has been at Los Blancos since 2005 and during his 16-year spell he won 22 trophies, but he will now leave the club as he could not reach an agreement with president Florentino Perez over a new contract.
However, Ramos's teammate Kroos has expressed his confidence in a return for the Spaniard, telling a podcast: "I'm also sure he will be seen again at Real Madrid, whatever his role. It would also be negligent if you don't get someone like that back at the club and keep him, as he can still make a difference in the future.
"I do not know Real Madrid without Sergio Ramos. It was inconceivable that this player was not going to finish his career at Real Madrid. I had hoped he would stay. I don't know where he will go, but I'm sure he will make a good decision.
"The seven years I was able to be with him as a player and as a person were incredible. Ramos was not only a top player but also the best captain I have ever seen, because he always fought for the team on the pitch and off it.
"If you ask 100 opposing strikers which defender they don't want to play against, Ramos' name will be mentioned quite often, and rightly so. So it was always good to have him in our team."
Ramos has scored 101 goals in 671 appearances for Real Madrid, after joining from Sevilla for £27m.