Brazilian midfielder Lucas Leiva has been linked with a move away from Anfield almost since he joined the club in 2007.
Liverpool are also prepared to offload Lucas, but Klopp wants to wait until the end of the transfer window to see if the player will be required as a back up option next season.
Reports in Turkey have suggested Galatasaray have already agreed a fee with the club and player, and are now waiting for the green light to complete the move.
Galatasaray’s board member, Levent Nazifoğ, has confirmed to Turkish website Yeni Safak that the club have a deal agreed with Liverpool for the transfer of Lucas.
He said: “We had taken initiatives to sign Lucas. We had agreed on everything with Liverpool. However, there are injury concerns in the team.”
The Brazilian midfielder has another year left on his contract at Liverpool, and it remains to be seen if Galatasaray are willing to wait for the Merseyside club to make a decision on him.