Murray said he "didn't like it" when First Minister Alex Salmond unfurled the Scottish flag behind Prime Minister David Cameron in the Royal Box at his historic Wimbledon victory, in an interview with the Sunday Times.
When asked who he would play for if Scotland left the UK, he said: "I don't even know."
He said Mr Salmond "seemed perfectly nice" when the pair met, but added: "I didn't like it when he got the Scottish flag up at Wimbledon."
"I started competing for Great Britain when I was 11. A lot of people forget that."
He would not be concerned if he has children and they do not have Scottish accents, he added.
"I wouldn't have thought that would be high on my list of priorities," he said.
Murray provoked a backlash in 2006 when he joked he would support "anyone but England" in the football World Cup, a comment he said that he later regretted.