The city wants to see if a settlement is possible in a lawsuit by thousands of workers who say they weren’t properly protected from toxic World Trade Center dust while cleaning up ground zero.

A lawyer for the ailing workers recently sent his clients a letter asking to authorize the talks with the city. Mayor Bloomberg said yesterday that holding talks doesn’t mean a settlement offer will be made.

“I can only tell you this: Every time you get sued, you always take a look and see” whether there is a way “to come to a settlement which would be in everybody’s interest,” the mayor said.

“There’s no reason to think that we can come to a settlement or reason to think that we can’t come to a settlement. Plain and simple, we’re just going to talk and explore.”

A lawyer for the workers, David Worby, declined comment yesterday.

City officials have pushed for the federal government to make funds available to treat thousands of ailing workers who have developed respiratory illnesses after working at ground zero in the months after the attacks of September 11. A victims’ compensation fund paid about 2,000 people sickened by trade center dust, but stopped taking claims after 2003.

The class-action lawsuit pending in federal court has over 9,000 plaintiffs, including about 100 who have died. It accuses the city and others who ran the cleanup of failing to provide protection from the toxic dust at the site.