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The All Blacks arrived back in Auckland from the Rugby World Cup in Japan today where they finished third.
Asked whether he would like to see Foster take over from Steve Hansen as head coach, Barrett said he was hoping for some 'continuity going forward'.
"He's a very intelligent coach. A great team man and hopefully we can have some continuity going forward," he added.
Barrett said Hansen's record with the team, 93 wins from 107 tests, speaks for itself.
"Steve's legacy is a very strong one. His win percentage speaks for itself. I think the biggest thing with Steve is the way he makes his players' feel. Trust and confidence. We know he 100% has our back. As a player that's all you can really ask for. He's taught me a lot along the way and I'm very lucky for that," the All Blacks fullback said.
Barrett, who was a World Cup champion four years ago, said he was happy to see the Springboks beat England in the final.
"To be fair we were probably supporting them. It's nice to see a southern hemisphere team and players that we are so familiar with and have friendships with lift the trophy. If it couldn't be us, we were encouraging them to win," he said.