Various Turkish newspapers including Fanatik have reported that the Istanbul Giants are preparing to make a move for the England international before the end of the season.
Glen Johnson has fallen out of Brendan Rodgers starting XI this season and expects to leave the club in summer.
“Of course [I expect to leave at the end of the season], I have no contract,” Johnson told the Liverpool Echo.
“I don’t think that will change but we have to wait and see. I have always been professional all season, always wanted to play and that’s still what I’m doing.
“I’ve got four more games and then let’s see what we do in the summer.”
The former Chelsea and Portsmouth defender has played 17 Premier League matches this season.
Galatasaray are currently second in the Turkish Super with 61 points in 28 games.