The 11-times capped Biggar has been in outstanding form in the RaboDirect PRO12 with 69 points so far including a superb 24-point haul in October's tie against Zebre.
Scarlets fly-half Priestland has undergone surgery to repair a ruptured Achilles tendon which has ruled him out of the Six Nations and potentially the Lions tour of Australia in the summer.
But Rees believes Biggar's performances in an Ospreys shirt warranted a chance to replace Priestland and called on the international team to put their faith in the 23-year-old.
"I think he is ready. I'd back him 100 percent for that Welsh shirt," he said.
"He would be the type to thrive on being a first choice fly-half. He has certainly done so here since we backed him. We trust him, he trusts us, and we tend to get the reward.
"He definitely needs a run of games. It's huge opportunity for him, but he needs to play well in this weekend's game with Toulouse, the big Christmas derbies and in our European matches next month.
"Then he can hit the ground running with Wales, which I'm sure he'll be able to do."
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