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England need a new partner for captain Alastair Cook, but Moeen has scored only 41 runs in his past three innings.
"I'm sure he'll show what he can do," said Root in the build-up to the first Test in Abu Dhabi, starting on Tuesday.
Alex Hales could also open the batting, but he made only nine on the final day of the tourists' final warm-up match.
All-rounder Moeen, 28, has made 749 runs at an average of 31.20 in his 16 Test matches.
"I think he's proven in Test cricket now that he's a valuable member of our batting side," said Root. "I'm sure he'll rise to the challenge.
"He's batted at six and eight and he's made valuable contributions in both positions."
England go into the three-Test series in the United Arab Emirates having beaten Australia 3-2 in the Ashes in the summer.
No visiting side has beaten Pakistan in a Test series since they relocated to the United Arab Emirates five years ago, with England beaten 3-0 on their only previous trip.
"It is going to be a big challenge and they're a very good side and very good in their own backyard," said Root.
"But we've shown over the last six months that we're capable of doing things that people don't expect us to and this is going to be no different.
"Against a very strong side like Pakistan, in their own conditions, we are going to have to play out of our skin, but we are more than capable of doing that."
Moeen Ali will "rise to the challenge" if he is picked to open the batting for England in the first Test against Pakistan, says vice-captain Joe Root.