The Rovers misfit scored in his side's FA Cup win over Barnsley in midweek, and has been linked with a number of Serie A sides, including Udinese, Bologna and Napoli.
"The rumours are absolutely not true," Giovagnoni told planetfootball.com.
"We are not interested in any strikers. We have enough strikers.
"There is no chance of seeing Grabbi in a Perugia shirt. We are not interested in this kind of player."
Meanwhile, Giovagnoni dismissed the likelihood of Giovanni Tedesco joining West Ham as "press speculation".
The Hammers are sending representatives to Perugia's Serie A clash with Lazio at the weekend, and planetfootball.com understand Glenn Roeder has plenty of potential targets.
Italian sources claim a bid of ‚é¼6 million for Tedesco (pictured) is to wing its way to Perugia president Luciano Gaucci, should the skipper convince the Londoners of his ability to perform impressively in The Premiership.
Defender Marco Di Loreto is also believed to be on West Ham's wanted list, as is Traianos Dellas, although the Greek star wants to remain in Italy.
