The Queen will attend the championships this Thursday for the first time since 1977, and the Scot has said he will "wait and see" what other players do before deciding whether to bow if he plays in front of her on Centre Court.
"It should be personal preference," said Murray.
"I'll have to wait and see. I don't want to be bowing and the person I'm playing with walk straight past or the other way around."
The custom of players bowing or curtsying before blue-blooded visitors in the Royal Box on Wimbledon's Centre Court was abandoned in 2003.
But an exception was kept in place for days when the Queen or Prince of Wales were in attendance - and the Queen's visit on Thursday will mark the first time either has been to Wimbledon since the rules were changed.
The men's and women's world number ones, Rafael Nadal and Serena Williams, have confirmed that they will bow and curtsy, with Williams claiming that she is already practising the traditional greeting.
Keen monarchists should not fear for Murray's loyalty to his sovereign, however: the Scot's thoughts on the matter are based on uncertainty rather than any republican sympathies, with the world number four adding that it would be a "great honour" to play in front of her majesty.
"I've never done that before so there would be a little bit of added pressure to play well," he added.
- Andy Murray