The Giallorossi have been upset by reports that they are set to lose the Morocco international, who is being courted by Bayern Munich, Manchester United and Chelsea
The Morocco international has been linked with a move away from the Italian capital all summer long, with both Chelsea and Manchester United said to be keen on signing the centre-half before the close of the transfer window.
However, it is now being reported that representatives from Bayern Munich are now in Rome to wrap up a deal for the 27-year-old, having been forced to step up their pursuit for another defender due to the knee injury sustained by Javi Martinez in Wednesday's DFL-Supercup loss to Borussia Dortmund.
Zanzi, though, says there is no truth in the rumours that Benatia is bound for the exit door at the Olimpico.
"Mehdi is our player," the chief executive told Corriere dello Sport. "According to some media sources he had already been sold, but instead he is training with us in a very professional manner.
"It's a shame about all these rumours. He is a great person and is behaving in the best possible way.
"The transfer market is dynamic and until September 1 we will evaluate every opportunity and ensure we are ready [for the new season]."
Benatia joined Roma from Udinese last summer and was one of the key players in last season's surprise second-place finish in Serie A.