Queen Elizabeth will make her first visit to Wimbledon since her 1977 silver jubilee year when she attends The Championships on Thursday.
The tradition of bowing or curtseying to the royal box ended in 2003, but with players not being obliged to show the usual gesture of respect towards the monarch, her subjects worldwide will be watching closely to see who adheres to traditional protocol.
A Wimbledon spokesman said that players would be asked whether they would like to bow or curtsey, but they will not be ordered to.
Andy Murray, Britain's most senior tennis pro, said he was ready to bow, but would not want to be involved in a scene should his opponent decline to do so, hinting at the minefield which might await the players.
"If the players want to, it should be personal preference, I guess," the world number four said.
"I'm sure all of the players might like to do it.
"I'll have to wait and see. I'll have a chat with the guys. I don't want to be bowing and the person I'm playing with walk straight past.
"You obviously need to have an agreement before you go on. I'll have to speak to the organisers about it.
"I don't want to get into some ridiculous argument over something like that.
"I'll see what the organisers want us to do and I'll do what they tell us to."
Queen Elizabeth is the club's patron, but the last of her three Wimbledon visits was in 1977 - the last time Britain had a winner in the singles.
The club's president, Prince Edward, the Duke of Kent - Queen Elizabeth's cousin and a grandson of king George V, who regularly undertakes duties on the sovereign's behalf - is the regular royal face at The Championships.
Players always used to bow or curtsey to the royal box on entering or leaving Centre Court, but the tradition was discontinued in 2003 in accordance with the Duke of Kent's wishes, though an exception remained if Queen Elizabeth or Prince Charles, the heir to the throne, was in attendance.
Rafael Nadal, from the Kingdom of Spain, said he would relish the opportunity.
"I would love to be (playing on) Thursday to have the chance to do it," said the world number one and the 2008 Wimbledon champion.
Asked if he would bow, he replied: "Sure. I respect everything."
The 2004 ladies' champion Maria Sharapova likewise seemed ready to take part in one of the old traditions that used to mark Wimbledon out as a special tournament.
"I've never had the honour to curtsey before. I think I was probably too young for that," the 23-year-old Russian said.
"It would be kind of fun. I'd love to do it. I think it would be an honour for all of us."
Meanwhile Venus Williams, the five-times Wimbledon ladies' champion, suggested she needed to bone up on the protocol.
"I'm an American. I'm not well-versed on English tradition," she said.
"Hopefully I won't get nervous. That would be my focus. But I guess I'll cross that bridge if it ever comes."