Emery has lost his first two Premier League games in charge of Arsenal to Manchester City and Chelsea.
Ozil has started both matches and disappointed so much in the visit to Chelsea that he was substituted in the second half.
The former Germany international only signed a new, three-and-a-half-year contract back in January which seems him earn a staggering £350,000-a-week.
And former Chelsea midfielder Burley says Emery has got a big problem on his hands with the 29-year-old.
“Unai Emery has inherited, inherited, a £300,000-a-week nightmare. He has,” Burley said.
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“He took him off (vs Chelsea) for a reason. You’re a man down without the ball and then when you have the ball, he doesn’t do enough.
“At time he does it, at times he will do something brilliant because he’s got brilliance in him, Mesut Ozil.
“But he’s inherited a £300,000-plus player and now he’s got to make a decision ‘what do I do with this guy?’. Where do you play him? How do you get the best out of him?
“You play him wide, he doesn’t track back. You play him in the middle, in the hole, he doesn’t go and press the deep-lying midfielder.”
Burley says it is time Emery thought about dropping Ozil, even if the board will wonder why the highest-paid player is not playing.
“That’s the decision (Emery) has to make (whether to drop Ozil),” he continued.
“At some point he’s got to go ‘I can’t play this guy, because he’s not doing what I want, and I’m going to be hired or fired at this football club on the decisions that I make. I’m new to England, they don’t care what I did in Spain or what I did in France. I’m new at this club and I’m following a guy who was very successful early on’.
“And the board, they’ll be saying like ‘well, we’re paying this guy’, so he’s got a decision to make.
“What’s the best for him or what’s the best for the team? Not what’s the best for Mesut Ozil or any of these big-time Charlies.
“At the end of the day, he needs everybody on board or he’s going to fail at Arsenal.
“If he doesn’t get them all on board or get them out, he’s going to fail.
“It is a huge job, we knew that already, but it’s a huge job.”