The coach's current deal expires in June as he is linked with bigger clubs.
Fenucci said, "The coach has been the architect of this growth and we hope that both he and the players will stay with us.
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"Thiago is very happy at Bologna, it's as if he had a longer contract than he actually has."
He also said: Doing all the best, a Bologna team in Europe, beyond the Champions League, would be a beautiful signal for all of Italian football. As Atalanta did in previous years, by preparing a serious corporate organisation, with the right people in the sports area, the coach and a group that goes beyond expectations, we can make a different path and give a new perspective to many clubs."