If you look at a picture of Mesut Özil and then an image of someone suffering from Graves Disease (aka thyroid eye disease), I think you'd probably conclude that he's not suffering from the condition.
The three points that make me think Özil isn't a sufferer are:
His eyes don't present any sign of redness or other symptoms typical to the condition
Graves disease is a condition where the physical effects often come and go, or sway in severity. Özil's eyes have remained pretty consistent.
A condition like Graves disease would have side effects like impaired vision, aches and pains, or sight loss. This would make become a professional athlete playing at the highest level pretty much impossible.