New Zealand fullback Beauden Barrett has voiced his support for Ian Foster's bid to take over from Steve Hansen as All Blacks coach, saying he would like to see "continuity" in the role, local media have reported.

Hansen ended his 16-year association with the team after New Zealand beat Wales to clinch third place at the Rugby World Cup on Friday.

The All Blacks returned to Auckland from Japan earlier on Tuesday and Barrett told reporters he loved working with assistant coach Foster.

"He's a very intelligent coach. A great team man and hopefully we can have some continuity going forward," the 28-year-old was quoted as saying by the New Zealand Herald.

Among the other candidates is Scott Robertson, who led the Canterbury Crusaders to three successive Super Rugby titles, and Warren Gatland, the former Wales coach who is heading back to New Zealand to coach the Waikato Chiefs.

Gatland's agreement to take the British and Irish Lions to South Africa in 2021 could rule him out until at least then, while Japan's Jamie Joseph has also been touted as a contender after leading the World Cup hosts to the quarterfinals.

Hansen won 86 percent of his matches in charge of New Zealand and was named World Coach of the Year four times.

"Steve's legacy is a very strong one. His win percentage speaks for itself," Barrett said. "I think the biggest thing with Steve is the way he makes his players' feel.

"We know he 100 percent 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."

Barrett said the All Blacks, who were beaten by England in the semifinal, were cheering for eventual champion South Africa in the final.

"It's nice to see a Southern Hemisphere team and players that we are so familiar with and have friendships with lift the trophy," he added. "If it couldn't be us, we were encouraging them to win."