Chief executive Mark Darbon says the R&A are having "ongoing dialogue" with Muirfield with a view to returning the Open Championship to the Gullane course.
Darbon also says there are "challenges" with bringing the event back to Turnberry.
Royal Lytham & St Annes will host the Open in 2028, with this year's 154th tournament taking place at Royal Birkdale and next year's staging at The Old Course at St Andrews.
Muirfield will host this year's Women's Amateur Championship from 22-27 June.
"We've got a great ongoing dialogue with Muirfield," Darbon said.
"There are some things we need to overcome to facilitate a modern Open Championship - the practice ground is one of those, along with a few on-course infrastructural points."
On US President Donald Trump's Turnberry, Darbon commented: "We really like the golf course.
"But there are challenges around staging a modern Open - primarily road, rail and accommodation infrastructure."
