Galatasaray were also interested in Johnson over the winter transfer window but could not make an offer due to reaching their foreign player limit.
Süper Lig clubs will however, be permitted to sign 14 foreign players starting from next season.
Galatasaray are planning to strengthen their right-back position over the summer.
Johsnson recently revealed that he will leave at the end of the season.
“I expect to leave at the end of the season, I have no contract,” Johnson was quoted as saying by the Daily Star
“I don’t think that will change but we have to wait and see.
“I have always been professional, 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 30-year-old is out of contract at the end of the season and Liverpool have not offered a new deal.
The England international joined Liverpool from Portsmouth for £10 million in 2009.
Serie A giants Roma have also been closely linked with a move for Johnson.
Galatasaray are currently third in the Süper Lig but have the chance to go top tomorrow against Akhisar as they have a game in hand.