Turan has long been linked with a switch to the Premier League, since he broke into the Gala first team in 2006.
Arsenal are thought to be very keen on the 23-year-old midfielder, who is tipped to depart Istanbul in the summer.
Keita, who only joined the club from Lyon last summer, has also become a huge fans' favourite.
The Ivory Coast forward is understood to have snubbed Everton to join Gala, but the Toffees are now understood to be back in for him along with Aston Villa.
However, the main interest from England is understood to come from Manchester City, with some reports claiming they are the club who have bid for 28-year-old Keita.
Gala president Adnan Polat would not reveal the identity of the bidders, but confirmed his club was not looking to sell.
"We have been offered 14million euros (£12million) for both players, but we do not intend to sell them," he told Milliyet.
Both players have been in superb form for Gala, who currently sit top of the Turkish Super Lig.
Trabzonspor 6/4, Galatasaray 6/4, Draw 11/5