The Turkish newspaper Fotomac state that initial talks between Galatasaray and the Blues have already taken place over the Ghana international.
The report goes onto state that Galatasaray want to include a €5 million buy-out clause in the loan deal.
The 23-year-old spent the first half of the season at the newly promoted Bournemouth but return to Chelsea after failing to break into the first team.
Atsu made just two league cup appearances for Bournemouth this season. the Ghana international made 13 appearances on loan at Everton last season.
Galatasaray are currently in third place in the Turkish Super Lig with 30 points in 17 games. The Lion’s are 11 points behind league leaders Besiktas.
The Lion’s are expected to make major changes to their squad following a disappointing start to the season.