Pappas wants to keep its business there. But, the city asked for proposals from other restaurants, and another group put in a higher bid than Pappas.
Pappas has questioned the process.
Christina Pappas and Mayor Sylvester Turner went back and forth on Tuesday.
"The structure of the rent that the city is asking is different. It is not apples to apples, sir. It is not apples to apples, so if you're trying to make it apples to apples, our current contract versus what's in the bid, they're not made the same way. It's an apple and an orange," Pappas said.
"No, it's not. I know apples and apples, and I know apples and oranges, and I know oranges and oranges," Turner responded. "But since you are criticizing the numbers, and you are here, let's deal with them."
The contract is worth half a billion dollars, and the city gets a cut of the money the restaurants bring in.
It's unclear when the vote will happen.