The young British tennis ace recently claimed the biggest title of his career so far at Indian Wells and the former British number one always knew that Draper had the ability to go far in the sport.
Speaking to The Guardian, Henman said: "I'm not really altogether that surprised. I think what is taking place now is the pieces of the puzzle coming together, and those pieces have always been there.
"But, if anything, it's just, perhaps, a few of the little injuries that have kept him away from building that momentum and tournament play.
"That's what I think, again, is exciting. He's seven in the world. He's just won his first Masters 1000 and to me, he still hasn't really played a consistent 12-18 months on tour. There's always been those interruptions.
"And I think when you take a little bit of a deeper dive into his game, there are very few weaknesses and still areas to improve on."
Henman has been appointed as the new vice-captain for Team Europe at the Laver Cup which takes place in September but has no interest in making a full-time move into coaching.
The former Wimbledon semi-finalist – who works as a pundit for various TV channels – said: "I think coaching is a far bigger commitment in terms of time, in terms of travel, and I've had those offers, but it just doesn't appeal to me.
"And that may change. I would never shut the door on coaching an individual player."
He continued: "I'm so excited about the Laver Cup because of the event itself, and the best players from Team Europe and Team World going at it. But there's a finite period.
"The television work I do is structured. It's around specific events and that balance, for me, is perfect."