De Rossi was sacked by Roma and replaced by Ivan Juric.
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Ranieri told Domenica Sportiva: "What surprised me is that he was given a three-year contract, it was supposed to be a long project.
"It's a shame that there isn't a football man in there who can unite the club and coach".
Then on the possible return of Francesco Totti, he added: "I'm not the one to judge. There are the Friedkins and they are the ones who must judge whether this person is needed."