Reports in the Italian press have claimed Buffon, 33, has been told he must accept a pay-cut if he is to stay at Juve, and Roma are believed to be monitoring the situation.
Buffon said in a TV interview last week that he would discuss any offers that arrived with Marotta, but the director general has now played down talk of a departure.
"We will be counting on Buffon for the present and the future," Marotta said. "We regularly talk with the player himself and his agent, Silvano Martina. It is not our intention to sell him."
However, Storari, who signed from AC Milan in a €4.5 million deal last summer, believes he has done enough to be considered Juve's No. 1.
Storari, 34, has been given chances as a result of Buffon's injury problems this season and, after playing a starring role in the 2-0 win over Roma, he told coach Gigi Del Neri that he deserves to be first choice.
"Only a blind person can't see what I am doing and I hope the coach is not blind," he said
Asked whether a lack of opportunities could see him join Roma rather than Buffon, he said: "I have never hidden the fact that I am a Roma fan, but the truth is that I am happy at Juventus and I want to earn some space here."
Del Neri, though, told Storari that he should not expect to be considered ahead of Buffon. "I'm not blind," he said. "Storari has a champion in front of him in Buffon. I want to thank Marco for what he did against Roma and I hope that he stays with Juventus, even if he doesn't play."