Ahead of next month's (Sep14) referendum, which could lead to a break-away, Byrne, who was born in Dumbarton, fears independence "might be a bit much to handle".
In an interview with The Evening Standard, he says, "As an outsider, my sense would be that by raising the issue again, Scotland can get a bit more autonomy and self-control, but complete independence might be a bit much to handle.
"I have lived in the States pretty much my whole life, but from my parents and everything, there's still an affinity to maybe a Scottish sense of humour, and some of the attitudes that go with that."
Byrne joins stars like Mick Jagger and Sting, who are opposed to Scottish independence. They added their names to a list of more than 200 celebrities who signed an open letter urging Scottish voters to keep Scotland as part of the United Kingdom.