Barrett and Crusaders teammate Codie Taylor have re-signed with New Zealand Rugby through until the 2027 World Cup.
Barrett is a leading contender to lead the All Blacks under new coach Scott Robertson, but a month out from the first test against England he is still recovering from a back injury that forced him out of the last few rounds of Super Rugby Pacific.
"I'm tracking all right," Barrett told a media conference in Christchurch. "I've had a bulged disc in my back but it's settling down."
Barrett's absence from much of the Crusaders' season played a part in their failure to make the playoffs and so he is motivated to get back playing.
"I'd be 50/50 for a game this week so I'm still getting a plan together for the next month on how I can get back to rugby. I'm super keen to get back and play - whether that's club rugby or facilitated training I'm not too sure, but I'm certainly keen to get out and play."
At Thursday's media conference he was asked if he would like to captain the All Blacks.
"It's something I'd be open to, but my focus right now is to get out on the park. It would be a huge honour. Those decisions are fully on Razor (Scott Robertson) and we've had conversations around the All Black environment, but ultimately the decision sits with him."
Barrett, 30, has played 69 tests since his debut against Ireland in 2016 and has 117 caps for the Crusaders, where he has led the team to four Super Rugby titles since taking on the captaincy in 2020.
Ardie Savea is the other obvious contender to captain the All Blacks this year.
Savea missed Super Rugby this year to play in Japan, but his Hurricanes teammate, former All Blacks halfback TJ Perenara - who could well be in line for a recall up to the national team this year and will face the Rebels in the Super Rugby quarter-finals on Saturday in Wellington - was asked if he would like to see Savea as All Blacks skipper.
"Yeah, I would. He's arguably the best player in the world. He's a really good friend of mine. I've seen the leadership he has within the environments I've been in with him. I was in the team when he captained the All Blacks for a while when we were overseas. His leadership in that and [the Hurricanes] environment and what he did for our group is amazing."
Though Perenara said Barrett would be a worthy All Blacks captain.
"Scott's a hell of a player. Has respect from a lot of the team. As someone who's won seven Super Rugby titles and had a lot to do with the Crusaders leadership group, he clearly leads their environment really well.
"So there's two clear candidates."
The All Blacks play tests against England in Dunedin on 6 July and Auckland on 13 July before a game against Fiji in San Diego on 20 July.
The Rugby Championship starts on 10 August.
