Having rolled out a successful double-captaincy policy in recent times, the Chiefs may change their approach in 2015.
Forwards Craig Clarke and Liam Messam guided the Chiefs to successive Super Rugby titles in 2012 and 2013.
Messam was partnered in the role by Aaron Cruden last year but Rennie is open to starting the new season with only one captain.
Messam, Cruden and another contender in World Rugby Player of the Year, Brodie Retallick, will all be unavailable for the Round One contest.
“We’ve got a lot of leaders within this group,” Rennie told Newstalk ZB
“But ultimately someone needs to have the C next to his name.
“We’ll sort through that the next couple of weeks.”