The former Chelsea star has reached the end of his 18-month contract and will not be signing an extension so departs the Turkish giants after failing to win the 2013-14 Super Lig
The former Chelsea striker signed an 18-month deal with the club in January 2013 after a short spell in China with Shanghai Shenhua.
"I leave the decision to the board to announce it because it is the same way they announce my arrival here in Galatasaray," he told the club's official TV channel. "It's hard because I think we have a lot more to do but that's life and I respect everything and everyone.
"For sure, the same way I respect Chelsea, the same way I respect Marseille, the same way I loved playing for Guingamp, it is the same way I will speak about Galatasaray. Everywhere I will go in the world it is the same way.
"I made a lot of new friends, good people, and I felt really good here. I feel really good here. It's sad. It's sad because, when people call you legend, call you with a lot of respect, it's always difficult to explain things.
"I'm not here to explain why. It's not my responsibility to explain why, but the fact is that I'm not sure next season we are going to be together."
The Ivory Coast international added: "I didn't come here for money. If I wanted money, I would have stayed in China. I came to Turkey to play football, to feel the passion again.
"I think I gave some happiness to our fans. I scored in against Fenerbahce and Besiktas, which are very important derbies. You can't make happy people all the time but I made them happy for 340 days out of 365 a year."
The 36-year-old won the Super Lig with Gala in his first half-season but the club's great rivals, Fenerbahce, pipped them to the title his season.
Recalling his initial move to the club in January 2013, Drogba explained: "Jose Mourinho and Wesley Sneijder had a big impact on my decision to sign for Galatasaray. Jose said to me: 'If Wesley is going, you go too,' so I came.
"It was a great thing to have a chance to play alongside [Sneijder]."