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Henry spoke at the Southland Graeme Dingle Foundation fundraiser in Invercargill on Wednesday and said he believed All Blacks coach Steve Hansen should step down after the 2019 Rugby World Cup.
"There comes a point where you have to move on," he said.
He paid tribute to Rennie and said he would be one of the best men for the job.
"He is one of the best all-round coaches we have seen in the past 10 years."
"He's one hell of a person and a great coach - the way he is able to connect with the players on another level is fantastic."
Henry noted Rennie's career had not come without adversity but said he would be a good fit.
Rennie was the head coach of the Chiefs in 2012-17 and led the team to back-to-back championships in 2012-13.
He left the Chiefs in 2017 to become head coach for the Glasgow Warriors, who play in the PRO14 and European Professional Club Rugby competitions. He led them to the semifinals of the PRO14 in his first year at the helm.
Previously, he coached the New Zealand under-20 team in 2008-10, winning three consecutive junior world championships.
Henry also paid tribute to Ireland coach Joe Schmidt and Wales coach Warren Gatland, saying both would also do a stellar job as All Blacks coach.
"They're both great; look what they have been doing with European rugby."
Japan coach Jamie Joseph and Super Rugby Sunwolves coach Tony Brown should also be looked at in the future, he said.
Henry said the combination of coaches was important in the All Blacks environment and said he was lucky to have Wayne Smith and Steve Hansen alongside him throughout his seven years with the side.
- Kayla Hodge