Boak met with Power coach Ken Hinkley at Alberton on Tuesday and signalled his intent to play on.
"This is my home," Boak said.
"This club is going in a really good direction led by Kenny and this playing group.
"We didn't finish this year the way we wanted to but this young group is taking this club forward and that is why I want to be a part of it.
"I still feel like I have plenty in the body and still have fire in the belly."
Port's campaign ended with consecutive finals losses after finishing third in the home-and-away season.
Boak was a solid contributor with 21 disposals in Saturday's semi-final loss to Greater Western Sydney, his 348th AFL game.
"It was good, a really good chat," the 35-year-old said of his meeting with Hinkley.
"Still working through some details but it was a really positive chat.
"This is a big decision so we will take as long as we need to."
Boak's successor as captain, Tom Jonas, retired with a calf injury preventing him from featuring in the finals.
The Power have delisted four players - Riley Bonner, Trent Dumont, Brynn Teakle and Nathan Barkla.
Bonner played 93 games but the 26-year-old fell from favour this year while ruckman Teakle departs after being drafted mid-campaign last season.
After 113 games for North Melbourne, Dumont played eight times for the Power last year but couldn't force his way into the club's AFL ranks this season.
Three rival players -Â Geelong's Esava Ratugolea, Essendon's Brandon Zerk-Thatcher, and Jordon Sweet from the Western Bulldogs - have told their clubs they want to join Port when the official trade period begins on October 9.
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