The Ayrshire club, hosting the Open in July, is consulting members over whether to end its men-only policy.
Last week, governing body the R&A decided Muirfield will not stage another Open after maintaining its ban on women members.
"We look forward to the review results," Johnnie Cole-Hamilton of the R&A told BBC Scotland.
"But we must give them, as a private club, the time and space to carry out that review so they can do it thoroughly and professionally.
"Royal Troon has always been aware that our view at the R&A is that golf should be open to all.
"We take our role very seriously and are very protective of the game and the future of the game."