The Netherlands international only joined the Turkish giant in January but has already been linked with a swift exit.
Sneijder joined the Istanbul club for 10 million euros from Inter in January but has fallen out of favor with the Netherlands ever since his move to Turkey.
Reports have suggested the 29-year-old could be tempted to rejoin former mentor Jose Mourinho - the man he won the treble under during the Portuguese's time in charge of the Nerazzurri - but Aysal and new Galatasaray manager Roberto Mancini are not interested in a sale.
"We don't have a decision or a desire to sell Sneijder. Mancini has not had enough time to find out about the squad. He doesn't want us to transfer somebody," Aysal told Bugun. "Sneijder has a temporary problem, I don't care about it. He is going to regain his form with us."
Mancini was named Fatih Terim's successor at the Turk Telekom Arena earlier this month after making a dreadful start to the campaign, which sees the club sitting in 13th position after having won the Turkish Super Lig title last season.
The arrival of Mancini has seen him linked with moves for a host of his former players, but Aysal denied speculation regarding a bid for Kolarov, whom Mancini coached at City.
"The rumors about Kolarov are all wrong," Aysal said.