Carroll, who is reportedly on £90k-per-week wages at West Ham, is out of contract at the end of the season. He has played just 26 minutes this season following his summer ankle surgery.
Galatasaray are looking to sign a striker and they would probably try their luck of signing him on a free transfer next summer.
However, West Ham should consider any potential offer for Carroll in January. Carroll is down the pecking order at the club, and he is unlikely to recapture his previous form especially after a long injury lay off.
A move away from the London club could be beneficial for all parties involved. The likes of Javier Hernandez and Lucas Perez are in front of him in the queue, and Carroll may find it difficult to get regular games.