The midfielder hasn't been registered with Fulham's Premier League squad for the first-half of this season.
Seri will be allowed to depart Fulham in January and Sabah says Gala are keen.
The midfielder had a previous loan spell with the Turkish giants and is highly regarded by coach Fatih Terim.
Indeed, it's claimed the pair have recently spoken, with Seri informing Terim: "I want to return to Galatasaray."
Gala will seek to buy Seri in January for around €2.8m.