The 36-year-old joined the Italian champions from AC Milan in 2010, but has made just three league appearances in each of his last two Serie A campaigns with the club.
It had been suggested that the Italian would depart as Gianluigi Buffon is the undisputed first choice, but Storari has quelled such claims.
"Of course all the market rumours are pleasing," he told Sky Sport Italia.
"But I still have a contract here and I want to stay. I have not played much because in front of me there is a phenomenon like Gigi."
Storari made 29 appearances during his first season at the club, deputising for Buffon who suffered a back injury in the 2010 World Cup.