Sinnott said he has had "very cursory discussions" with Fire Chief Tony Pol about which company to shut down, but that no decision has been made.
Firefighters at the closed company would be reassigned to the five remaining companies in the city to meet a new minimum-staffing mandate outlined in the award, he said.
The award would require the city to hire as many as 24 new firefighters at a cost of $1.7 million for one year alone, if a company were not closed, Sinnott said.
"We have to comply with this order, and we don't have the resources to hire more firefighters," Sinnott said Monday.
Sinnott's decision followed a ruling by Erie County Judge Shad Connelly holding the city in civil contempt of court for not complying with the staffing mandates outlined in the arbitration award. Those mandates were to go into effect Jan. 1.
In the March 11 ruling, Connelly ordered the city to implement the award within 30 days. He also denied a request by the city to stay an earlier order affirming the staffing mandates.
The city had argued that the cost of the staffing mandates would cause the city "irreparable harm," and asked for the stay to postpone enforcement of the award while it appeals the award in Commonwealth Court.
"It's conceivable that massive amounts of overtime could be used for many months while the (appeal) process occurs," said Richard Perhacs, the lawyer who represented the city during its most recent arbitration with the union. "The problem is, the city doesn't have the money for that."
Pol declined to comment.
John Bielski, one the Philadelphia-based lawyers working for the firefighters union on the case, called Connelly's order "a great win for the firefighters and the citizens of Erie."
"They sought in ... arbitration safety and staffing provisions to protect them and ultimately to protect the public," Bielski said. "The city's failure to abide by those ... was prohibiting those provisions from being implemented."
Told of the mayor's plans to close a company, Bielski said, "We will see what the mayor does and we will take appropriate action as we see fit."
Dave Chiaramonte, president of the International Association of Fire Fighters Local 293, could not be reached for comment Monday.
The arbitrator's award, part of a four-year contract awarded in January 2009, required the city to adjust firefighter staffing by adding a fifth firefighter to every rig if the city maintains six or fewer companies, or by adding a seventh company, starting Jan. 1.
The arbitrator also ruled that the city must discontinue its "dual companies" in favor of single companies for safety reasons. Dual companies are those in which a single crew can respond with a ladder or pump truck, depending on the call. Two of the city's six companies -- Central Fire Station at 208 W. 12th St. and South Central Fire Station at 3507 Peach St. -- are dual companies.
City officials maintain the mandate requiring an additional firefighter per rig or the creation of a new company could force the city to hire as many as 24 new firefighters, at a cost of $1.7 million for 2010 alone.
Richard Poulson, another lawyer working on behalf of the firefighters' union, disputed those numbers and, in the past, has offered scenarios in which the city could fulfill the requirement with either no new hires or fewer hires.
Poulson acknowledged that by doing so, the city likely would have to rely on more overtime -- something he said he doesn't necessarily advocate. The city could consider a combination of new hires and additional overtime, he said.
But the question of cost isn't the only logistical issue the city is facing. Figuring out which company to close will depend on how and where equipment is moved after the dual companies are dissolved, among other factors, Sinnott said.
The city's current dispatch plan is also based on the current configuration of six companies and will need to be reviewed and changed in consultation with the Erie County 911 Center.
The city will decide which company to close based on a revamped dispatch plan and "what works best to get the right amount of equipment and men (to fires), wherever that might be," Sinnott said.
"That means looking at the entire system and how we can change it to meet the requirements but also to make sure we're still getting to all parts of the city in a timely fashion," he said.
Sinnott declined to comment about the possibility of shutting down Engine Co. 11 at West Eighth Street and Kahkwa Boulevard, a scenario that had been discussed during previous talks of consolidation and closure.
Whatever happens, safety and quick response times -- four minutes is the target -- remain top priorities, Sinnott said.
Closing down a company "is not what I would have chosen to do. The current circumstances are a lot better, and I feel it's not the right thing for anyone involved," he said. "I don't think firefighters are getting what they want, and we're certainly not getting what we want. It's an unfortunate result of how this process has gone.
"We obviously still need to get to all parts of the city in four minutes, and we're not going to compromise time and safety," Sinnott said. "We're going to make sure we do it properly."