The states that the Fifa accredited football agent Ayhan Yeşilbaş has offered the Cameroon international to the Istanbul giants.
Galatasaray are on the lookout for a new defensive midfielder following reports linking Felipe Melo with a move to Inter Milan.
Song provided three assists in 28 appearances while on loan at West Ham last season.
The 27-year-old has previously played for Charlton Athletic, Bastia and Barcelona.
Song is currently contracted to Barcelona until 2017 but is expected to leave this summer after falling out of favour with the La Liga champions.
Southampton are also involved in the race to sign the defensive midfielder according to the Mirror.
Galatasaray won the league title for the 20th time last season and secured a place in the Champions League group stages.