PGA Tour commissioner Jay Monahan and Yasir Al-Rumayyan, the governor of Saudi Arabia's Public Investment Fund, which bankrolls LIV Golf are both playing in the pro-am event in Scotland.
Monahan and his partner American Billy Horschel will play in the same group as Al-Rumayyan and South Africa's Dean Burmester in Thursday's first round at Carnoustie.
McIlroy, who will play alongside his father Gerry, is set to play with both Monahan and Al-Rumayyan over the course of the weekend.
LIV has lured away a number of the world's top players to the breakaway tour thanks to the huge signing bonuses and prize money on offer.
The PGA Tour, DP World Tour and PIF have been engaged in talks since 2023 in a bid to bring the world's best back together on a regular basis.
"It's a great thing and a good sign that Jay and Yasir are playing together on Thursday," McIlroy told the BBC during a practice round at St. Andrews on Wednesday.
"There's no better place than the home of golf to get everyone together and talking."
McIlroy was often the centre of attention as the leading representative of the PGA Tour in the early months of LIV's attempt to lure away big names.
The world number three has since decided to take more of a back seat but hopes negotiations can proceed quickly to start 2025 with clarity.
"Maybe it is going too slow for the people who follow golf. But I think in the business world deals of this size take time," added McIlroy.
"It's a pretty complicated deal, but I think we'll know more by the year's end hopefully.
"We are in October, so three months to get something done and start 2025 with enthusiasm and all move forward together."
