The highly-rated striker made two appearances for the first team at the end of last season but was sent out on loan to Bristol City this term.
The 19-year-old has impressed during his time with the Championship club scoring 18 goals in just 32 league appearances.
It has been suggested that Abraham could be involved in the first team at Stamford Bridge following the summer but now reports in Turkey have claimed that Galatasaray want him on loan.
The Turkish heavyweights are managed by Croatian Igor Tudor, who is a friend of Chelsea boss Antonio Conte following their time playing together at Juventus.