At a hearing in Lansing, Mich., the state capital, on Tuesday, the Detroit City Council tried to persuade the state not to take over the city's finances.
But Snyder is widely expected to go ahead and appoint an emergency manager as early as this week.
Detroit, the birthplace of the U.S. auto industry and Motown popular music, has suffered from a sharp population decline that has left the city with falling tax revenue, rising crime and a costly and outdated government structure.
According to a report commissioned by Snyder, the city of 700,000 has "operational dysfunction" in its government, a crushing debt of $14 billion and a current fiscal year deficit of $100 million.
An emergency financial manager in Detroit will have authority over the city's fiscal affairs, including contracts, asset sales, layoffs and consolidations.
The manager can also recommend the city file for bankruptcy protection. That move, if allowed by the state, would mark the biggest Chapter 9 municipal bankruptcy in the United States. (Read More: US Municipalities That Went Bankrupt)
The Detroit Free Press earlier Tuesday reported that Orr was the top candidate for the job. Detroit Mayor Dave Bing has picked Jones Day as the restructuring counsel for the city.
The newspaper cited several sources with knowledge of the search process who requested anonymity. A source with direct knowledge of the decision confirmed to Reuters that Orr was the top choice.