Matthaus believes Ter Stegen will leave Barca this summer after the arrival of Joan Garcia from Espanyol and the imminent contract renewa of Wojciech Szczesny.
He told Sky Deutschland: "Since Szczesny will probably renew his contract, I expect Ter Stegen to leave Barcelona.
"Galatasaray would be one of several options: they have underlined their ambitions by signing (Leroy) Sané and will play in the Champions League next season.
"Then next season there will be six English clubs playing in the Champions League, and none of them have a goalkeeper strong enough to say: 'Ter Stegen is not of interest to us'.
"I don't know what Manchester City's plans are , but I think they are not very happy with Ederson. I think ter Stegen could definitely be the Citizens' goalkeeper for the next three or four years."
Ter Stegen still world class
Then Matthaus stated: "Marc-André ter Stegen's situation at Barcelona is uncomfortable for him.
"He has returned in great shape after a long injury and, especially in the Nations League against France, he showed that he is still a world-class goalkeeper at 33 years old.
"But Joan Garcia, who Barcelona signed from Espanyol, is nine years younger. He is already part of the Spanish national team and is expected to play for them in the future."