Gilardino has been dismissed by Genoa this week after leading the club to promotion last year.
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Mutu said, "It's part of a coach's life, I've been there too. Sometimes in life an episode like this can bring you something more, he'll analyse his time at Genoa and obviously become stronger. I hope Gila becomes a great coach."
Asked himself about a return to the Viola, the Romanian said: "Returning to coach in Florence one day? Well, I hope so, that's the goal. But let's leave these things aside, (Raffaele) Palladino is doing well, I've seen him motivated, he'll do well and the club has faith in him."