Henry has played an instrumental role in guiding Ulster to seven wins from their seven matches this season, including five in the RaboDirect PRO12 which has taken them to the top of the table.
And Anscombe, who was a flanker in his playing days, cited Henry's last three performances - against Glasgow Warriors, Castres and Connacht - as proof of his form.
"That's three in a row and I'll be disappointed if he's not in the green jersey in a couple of weeks' time," Anscombe told the Irish Independent.
"He has shown enough to justify an opportunity to run out against South Africa, there's no doubt about that.
"I think he has matured and he's ready. He is in great form at the minute and I believe that if he got that opportunity he really could show that he has got something to offer."
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