The departing Arsenal midfielder is scheduled to undergo the second phase of his medical today ahead of finally penning a contract with Fener to 2024.
However, Koc cautioned: "The dream has not come true yet. We are taking important steps in the right direction there too. I welcome Mesut and his family both to his club and to his hometown.
"The arrival of Mesut is a great transfer in football and also a big brand transfer. We have seen this since Saturday evening.
"Mesut, with his son in hand, has come home. He has come home to his hometown and to the team he has supported. I see a big difference there and I really care about this difference."
He continued: "Fortunately, no injuries.
"I want to thank our fans. They supported us with full force. The plane took off, arrived in Turkey and, in total, 1 million 880 thousand people checked where the plane was, 1 million people singularly, 312 thousand people connected to the (flight tracking) application at the same time. This is one of the two records.
"Fenerbahce supporters believed, he has great expectations, I hope Mesut will return that expectation."