Johnson started his career at West Ham but left the club to join Chelsea for £6million in 2003.
The experienced fullback has been at Liverpool since 2009 but has fallen out of favour with Brendan Rodgers following the managers decision to use a defensive back-three.
Johnson has struggled for first team football and fallen behind the pecking order in the Reds defence.
The Daily Mail have also reported that West Ham could also be tempted to make a summer move for the England international.
Johnson is available as a free agent in the summer with his contract set to run out at the end of the season.
Galatasaray are reported to be considering making an offer worth €2.5 million per-season for the 30-year-old according to Eurosport TR.
Johnson recently confirmed interest from foreign clubs but remains undecided on his future.
“No talks. At this point I have no idea [where I will be next season]. I haven’t thought about it,” Johson was quoted as saying in the Guardian.
“There are talks. It would be great for the kids to go abroad but I am not thinking about yet as we have two months left here and I’ll think about it after that. We will have to wait and see.”