"You pick the team first and then you pick the captain," Connolly said.
"Whatever else I say beyond that could be misconstrued, there is still so much footy to be played before we have to make that decision."
With 127 Tests and the experience of three World Cup campaigns to his credit, Gregan is the prime candidate to reclaim the role from Brumbies team-mate Stirling Mortlock, who led the Wallabies on the tour of Britain and Europe in November.
Gregan said he would be thrilled to named as skipper but he admitted he was more focused on his side's Super 14 season opener against the Chiefs in Hamilton next week.
"If I get it (the captaincy), it's a wonderful, wonderful honour," Gregan said.
The other name thrown into discussion has been NSW Waratahs skipper Phil Waugh, who stepped up to lead the Wallabies against Wales in Cardiff, while Mortlock was injured, and received rave reviews for his leadership.
Meanwhile, Wallabies veteran Stephen Larkham is continuing to work on the new playing style that backline tactics assistant coach Scott Johnson has developed with the team.
The Brumbies pivot is hoping to practice the tactics and hone his skills during the upcoming Super 14 season in preparation for the World Cup.
"It's coming through the Brumbies ranks now," Larkham said.
"I think that's important. I'd hate to play a whole season of Super 14 using one style and then having to try to adapt all over again with the Wallabies."
Connolly claimed Larkham would be provided with every opportunity to rest ahead of the World Cup event later in the year.Â
"Bernie (Larkham) is a world-class player and incredibly important to our chances at the (Rugby) World Cup," he told The Australian newspaper.