Rennie will formally assume the role next month and he revealed the team will be selected before a skipper is chosen.
The incoming Wallabies boss also expressed disappointment that Izack Rodda and Harry Hockings will not be at his disposal after refusing to accept pay cuts that were signed off by the Rugby Union Players Association and Rugby Australia.
After a tough spell under Michael Cheika, beaten 2019 Rugby World cup quarter-finalists Australia will hope for a brighter future under former Glasgow Warriors coach Rennie but he is not sure who will lead his team.
"We haven't spoken about captaincy at all, and I've spoken with Hoops a lot on various things," Rennie said when asked on a Zoom call if Hooper would stay on as captain.
"All we've talked about at the moment is earning the right to play, so it's about playing well enough to win the jersey and then we'll sort out who the captain will be."
Hooper recently stepped down from the captaincy role with the Waratahs and Rennie believes the flanker's performances have improved as a result.
"Clearly, he's not doing it at the Waratahs, and that's been good for his game to be honest, I think he's played really well. He's still leading, no doubt, he just hasn't got the 'C' next to his name," Rennie said.
"So, he's a strong contender for captain but we haven't firmed up any decisions around that; we'll just work out what the team is and then we'll select the captain. But there [are] lots of good leaders in amongst that group."
On the issue of Rodda and Hockings, both of whom have come in for heavy criticism, Rennie felt perhaps the full story had not come to light.
"I've spoken a lot to Izack, I don't know what's been reported, I don't tend to read a lot of papers, but the full picture probably hasn't been painted," he said.
"I had a good chat to him last week, but he's gone and the whole situation is really messy and could have been handled a lot better. So that's disappointing.
"With young Harry Hockings gone, who I think could have been an outstanding international lock, and with Izack gone, and when you look at guys like Rory Arnold heading off last year, there's certainly an opportunity for some guys [locks] coming through. So not ideal but it is what it is, and we've got to get on with it."