The Netherlands international only joined the Turkish giants in January but has already been linked with a swift exit, though the club are keen to hold onto the 29-year-old
Sneijder joined the Istanbul club for £8.5 million from Inter in January but has fallen out of favour 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 Gala boss Roberto Mancini are not interested in a sale.
The 72-year-old told Bugun: "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.
"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 them sat in 13th position having won the Turkish Super Lig title last season.
The arrival of the Italian has seen Mancini linked with moves for a host of his former players but Aysal also denied speculation regarding a bid for City left-back Kolarov. "The rumours about Kolarov are all wrong," he added.