Depth at lock is a concern as Sam Whitelock is approaching the end of his career, while Brodie Retallick is unavailable until late 2021 having signed a contract allowing him a two-year playing sabbatical in Japan.
Barrett and Blues captain Patrick Tuipulotu are the only other locks playing top-class rugby within New Zealand with any test experience.
Barrett also confirmed he won't skip Super Rugby and follow the trail blazed by Whitelock and Retallick, as his contract doesn't include a sabbatical.
"I would like to put my hand up and take charge of the second row in the All Blacks and that is certainly a big challenge,'' Barrett said.
"It is something that excites me, to be able to potentially lead a pack at All Black level. And run the lineouts.''
Barrett returned to training for the Crusaders on Monday as they prepared for the launch of a 10-week domestic competition involving New Zealand's Super Rugby teams on June 13.
"There's a lot of energy around the camp, the boys are fizzing," said Barrett. "There is still quite a bit of pre-season before we start, over lockdown we trained pretty hard and ran well in the Bronco [fitness] test yesterday. We're still training in bubbles which is not normal, like a lot of workplaces I guess.
"There's been a lot of talk about the derbies being tough and physical and demanding but its bloody exciting for the New Zealand public and for us players too. It's what the rugby public want. There's going to be some awesome rugby on display."
Barrett took over the captaincy at the Crusaders from Whitelock this year and led them to the top of the New Zealand conference when the competition was suspended after seven rounds due to the Covid-19 pandemic.
He is the sixth All Black to re-sign recently, joining brother Beauden Barrett, Retallick, Whitelock, experienced midfielder Anton Lienert-Brown and promising one-cap prop Tyrel Lomax.