The Ghanaian is due to leave the country soon with a view to finalising a move, according to a source.
"There are a few things that need to be tied up before he jets off to Turkey," says the informant.
"If things goes well, he will leave next week."
Morrison has failed to live up to expectations in the PSL after joining the Sea Robbers on a three-year deal in August 2016 from Congolese giants AS Vita.
Pirates have already released fellow attacker Thabo Rakhale and Nkosinathi Mthiyane to Chippa United this transfer window, while utility player Abbubaker Mobara has been linked with a switch to Bidvest Wits.
Defender Ayanda Gcaba's future with Bucs remains uncertain with his contract at the club set to expire in June.