Tudor was sacked by Juve this morning after Sunday's defeat at Lazio.
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Asked about a replacement, Cobolli Gigli told TMW: "The one person I wouldn't like because he's always had a negative attitude towards Juventus is Mancini. If I were to make a selection, I think he's the most relevant; despite my hesitations, it's a good idea.
"He's never been polite to Juventus, he knows his job, but I won't forget. I'd rule out (Luciano) Spalletti."
Asked about Raffaele Palladino, he added: "He's done good things, even with Fiorentina. He left at the end of the season, but I think the way he did it was a polite way to hide a spontaneous exit.
"He has a lot of good will, but not a lot of experience. Between the two, I'd choose Mancini."