They made their argument Wednesday to Circuit Judge Kevin Carroll. He asked lawyers from both sides to submit additional written arguments by the end of next week before he makes a ruling.
Carroll last month declined to rule on a challenge to the budget provision because it had expired.
Gov. Rick Scott's administration, though, is moving ahead with the privatization, claiming that the Department of Corrections has that authority under existing law even without the budget provision.
The department has issued notices of intent to award contracts to two private companies that responded to requests for proposals sought under the expired budget provision.
