And de Rossi has indicated the 24-year-old could be in line to feature in his first GUINNESS PRO12 fixture on Saturday when Zebre welcome Edinburgh to Stadio Sergio Lanfranchi.
De Rossi said: "I'm pleased with Cook's approach; both with the team strictly from a sporting level and that he is immediately ready both physically and mentally.
"Jean has shown desire to integrate with the group in order to show the technical staff that he is already in the race for Saturday.
"In these early workouts he confirmed his great defensive skills and his [ability as a] jumper."
Cook started his career with Free State Cheetahs before moving to the Bulls for a couple of seasons.
The forward, who was part of the South Africa squad at the 2011 Junior World Championships, then returned to the Cheetahs in 2014.
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Guinness PRO12 Zebre News
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