TMW says De Rossi will sign his Genoa contract today.
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The former Roma coach will initial a deal to the end of the season, with an option for another year.
De Rossi will succeed Patrick Vieira, who was dismissed last week.
There had been talk of Genoa sticking with caretakers Roberto Murgita and Domenico Criscito after Monday night's win against Sassuolo.
However, Genoa are keen to have De Rossi in the dugout for the weekend clash with Fiorentina.