The company has previously said it would fight all personal-injury litigation over the drug's harmful side effects.
"Certainly we will make reasonable decisions about how to proceed in defending each one of those cases," spokesman Kent Jarrell told The Associated Press, adding that Merck has "no intention of entering into any kind of global settlement."
Watch 60 Minutes on the Vioxx controversy. 7 p.m. Sunday, EDT.
Merck's general counsel, Kenneth C. Frazier, told The New York Times in Friday's editions that Merck would consider settling suits brought by people who took Vioxx for long periods of time and had few other risk factors for heart disease.
New Jersey-based Merck pulled Vioxx from the market nearly a year ago when a study showed it could double the risk of heart attack or stroke if taken for 18 months or longer.
Lawyers involved in a Vioxx case in federal court in New Orleans said at a hearing Thursday that nearly 5,000 lawsuits have been filed against Merck, and the number is growing. A trial starts in New Jersey state court next month, followed by the federal case in New Orleans in November.
A jury in Texas last week awarded $253.4 million in damages to the widow of Bob Ernst, who died in 2001 of irregular heart beat, or arrhythmia, after taking Vioxx for eight months.
The bulk of the verdict, $229 million, was punitive damages, which are capped under Texas law. After the caps are applied, the award won't exceed $26.1 million.
Merck has said it will appeal.
Merck has set aside $675 million to fight the rash of suits, but analysts think it may have also need to reserve funds to pay verdicts.
CBS News Legal Analyst Andrew Cohen said Merck now has to figure out how it will defend itself in all these other lawsuits.
"Clearly, the legal strategy it had used in this case was a catastrophe," Cohen said. "Whether that means we'll see more settlements, or a completely different legal defense, or something even more dramatic like bankruptcy is the question going forward."