Civil District Judge Kern Reese said he would give the mayor one week to offer a plan to pay the city's firefighters before a house arrest sentence, the report said.
Last year, the city agreed to pay $75 million to satisfy back pay but failed to deliver.
The city has faced decades of litigation over how it would fund the firefighters' pension system. Last month, the mayor proposed a $42.25 million plan that could put an end to the problem. However, it is contingent on the approval of a property tax increase by New Orleans voters in a March 2016 election, the paper reports.
"This is a legal issue," Reese said in court. "We all have responsibilities and those responsibilities have to be met."