Bravo is returning to Bayer Leverkusen after two seasons with Real Madrid on-loan.
Last term he played for Arbeloa with the U19s and told Marca: "Yes (he can coach the first team).
"Arbeloa knows a lot about football. To make myself clear and without comparing, he is a bit like Guardiola, in the sense of being a football 'madman'. He understands tactics very well, knowing how to press and looking for ways to attack depending on what the opponent is doing.
"And, above all, that emotional intelligence of knowing how to lead people, a dressing room like the first team's would be perfect for him. And he also knows the club very well. Right now Ancelotti is doing very well, but in a few years I do see him there."
Asked about a message for Arbeloa, Bravo also said: "First, I would give him a big hug. Then I would thank him in capital letters for everything he has done for me, especially on a personal level rather than in football.
"Because the boss is not going to teach me how to shoot, but as he understands you so well, he has experienced so many situations in football and has been in so many dressing rooms, he has given me advice on how to deal with frustrations, how to behave in a dressing room or how to act."