Tredrea, 29, became the third stand-alone leader of the Power in 2006 when he took over the prestigious number one guernsey from Matthew Primus.
Coach Mark Williams and new CEO Mark Haysman said the club would be open to the idea of multiple captains, but Williams advocated the more traditional single figurehead model.
"If you look at what's going on around Australia, Michael Voss comes in at Brisbane and scrubs the four captains to make one, so I'm not sure there's a single 'best' way of doing it," Williams said on Tuesday.
"They used rotations in the captaincy at St Kilda. [Former Port Adelaide Magpies captain] Geof Motley wore number 17, so you don't have to wear number one.
"I'm open to either way, but if you sit in front of the locker next to me in the locker room, you'll see there is a number one on that locker and that the names underneath it are singular, not plural.
"I can understand why some people do it. It wouldn't be by number one choice and it's not my number one choice because the buck has to stop with someone.
"It might be old school, but if you look at the past couple of grand final teams, you would've seen Tom Harley take the cup for Geelong and Sam Mitchell last year. When you say it [my belief] is old school, I'd say it's probably en vogue and the way the top two sides are doing it right now.
"But we're always open and easy to move forward on different ideas at this club, so nothing is set in stone."
Tredrea's successor is expected to come from within the Power's 2008 leadership group, which consisted of Shaun Burgoyne, Brendon Lade, Chad Cornes, Kane Cornes, Dom Cassisi, Tredrea and the retired Michael Wilson.
While there may not be an obvious standout for the captaincy next season, Williams said several players embodied the necessary requirements to lead the club.
"There are a wide variety [of candidates] and when you look at the prerequisites or traits of what makes a good leader, all of those guys have seven out of 10, so it's a question of which ones you don't have and which are most important," he said.
"No one comes with 10 out of 10. They build into the role and they learn. Tredders developed remarkably over the time he was captain.
"And Warren has been fantastic for the club, without any doubt. When Matty [Primus] did break down [in 2004], basically there was a bit of a void there, so to have Warren ready and available was great for us.
"It's hard to reflect on what you, yourself, have brought to the club, but I think his preparation and dedication to being the absolute best he could is the thing that will go down in my mind."
Williams said there were likely to be minimal changes to the Power's leadership group, which will be voted on by the players this week.
The club's leadership program, which was deemed to be somewhat ineffective last season, will now be co-ordinated by long-serving trainer David Arnfield with the assistance of several outside consultants.
Port Adelaide's new captain is expected to be named in late December/early January.
