I could not find a definite answer on this. There is no source that lists the native language of Roman emperors, however using the provinces in which they were born, the names that they were given, and the ancestry of their parents, we can make an educated guess. The earliest emperor who was both born in a Greek settlement, and given a Greek name was Diocletian. He was born in Salona, which was originally established as a Greek trade outpost in modern day Croatia. The birthname given to him by his parents was Diocles, a fairly common Greek name. This gives us a strong indication that he natively spoke Greek. I hope that this helps.