The free agent is hoping to secure a move to a club in the coming weeks.
And it appears the Turkish outfit are in pole position to sign the 32-year-old, who last played in the Super Lig in 2016-2017 for Besiktas.
Babel scored five goals for Fulham in 16 league games, but could not help them avoid relegation.
"They have the best offer at the moment. I don't have to make a secret of that," he told Algemeen Dagblad rumours linking him to Galatasaray.
"But there are also discussions with other clubs.
"It wouldn't be the first time in football or my own career for things to go differently than expected, so I will just have to wait and see."