The Boxing New Zealand selector is a firm fan of Parker and he hopes his friend can upset Anthony Joshua in their heavyweight unification bout in Cardiff on Sunday.
Joshua has two of the four major boxing titles and Parker has the World Boxing Organisation title, so there is a lot a stake.
The winner potentially faces a showdown with American Deontay Wilder, who has the other major title and is undefeated with 39 knockouts in 40 professional fights.
Perhaps most impressively, he got up off the canvas to beat Wladimir Klitschko in April last year. Klitschko dominated the division for 10 years until his surprise defeat to Tyson Fury in November 2015.
His battle with Joshua was one of the better heavyweight fights in recent memory.
Joshua knocked him down in round five and eventually stopped his opponent in round 11.
But the British boxer spent some time on the mat in round six and took a couple of rounds to recover before he was able to launch his successful assault.
Henry is well aware of the challenge ahead for Parker but said he had to be hopeful for the likeable New Zealander, who has never been knocked down in a professional fight.
''I'm really hoping Joseph Parker wins for obvious reasons. He is my friend but beyond that it would be good for boxing in New Zealand,'' he said.
''My thoughts on it are it would be good to see Joseph finish him in the early rounds because Anthony Joshua is going to be a hard guy to beat if it goes into the later rounds.''
Parker's past three fights have gone the distance whereas most of Joshua's fights have been over awfully quickly. But Henry felt Joshua showed his tenacity in the Klitschko fight and will have the stamina if needed.
''I do believe Parker has the ability to put him away if he can catch him early. That is when he will be at his freshest and still have his power.''
Parker looked to have plenty of power early in his career but since stepping up to fight better-calibre opponents, that power has not always been obvious. And that is a worry when you compare his vigour with the ability Joshua has to dispatch his rivals.
''They both have a good knockout record but it just seems the guys that Anthony Joshua was fighting were better fighters.
''I'm wondering if that will make a difference in the fight. With Anthony Joshua being such an athlete, even if he can't put Joseph away, he could steal five or six of those later rounds with that extra reach he has.''
Joshua is 5cm taller than Parker but his reach advantage is even more significant. That means Parker will have to find a way to get inside without getting hit too often.
''Parker has to box smart and have a good, tight defence. He needs to move off the ropes well and get out of range. And when he has the chance, he has to start landing those shots.
''He can't let rounds slip by without landing punches. He has to get inside those long arms. You can't sit there and wear those punches from mid-range.
''So he has to find a block or slip, and get inside and land his shots to keep the pressure on. But that is easier said than done because Joshua can really box.''
When pressed on whether Parker could really win, Henry hesitated before eventually falling in behind Team Parker.
''I think he can. You've got to have that hope for him. I'm going to back him and say he can.''
