The Brazil centre-back claims that Barca coach Tito Vilanova personally told him last season that he wanted to sign him.
Meanwhile, the player's agent, Paulo Tonietto, has urged the Spanish champions to make contact soon if they want to bring Silva to the Camp Nou.
"It has been said that Tito really wants to sign him and, if that's the case, someone should speak up," Tonietto told radio station Rac1.
"If someone wants to buy someone, it's not going to happen while they're sitting at home watching television."
However, the Ligue 1 champions are not willing to let their star defender go, according to Al Khelaifi.
He told Sport: "Thiago Silva is not for sale. He will stay at the club until the end of his contract.
"The problem is not that Barca are not offering us enough money, the problem is we don't want to negotiate his sale."
Happy in Paris
The PSG president affirmed he is in close contact with many of the club's players, including Thiago Silva.
"I spoke to him today [Wednesday] to congratulate him on the success he has had with his country in the Confederations Cup, and he told me he was very happy in Paris," he said.
Al Khelaifi also insisted PSG would reject a reported 32million euros offer from Barca because they have ambitions of building on their Ligue 1 triumph last season.
"We won't evaluate it or contemplate it. We won't even sit down to negotiate," he said.
"Selling is exactly the opposite of what we want to do. Our intention, after winning the domestic league title, is to fight for other more ambitious goals and make more signings."