The company says its $1bn offer to the music industry is based on the number of files traded over its service.
Napster officials say they are proposing to pay five major record companies $150m per year for five years, using the revenues generated by a new subscription service. Under the proposal, independent labels would get $50m annually over the same period.
EMI, BMG, Sony, Warner and Universal said the online company costs them billions of dollars in royalties, but Napster says its users, some 50 million of them, are not infringing copyright.
Of the five, only BMG, through its parent company Bertelsmann, has reached an agreement with Napster. They are now partners.
Bertelsmann has promised to make its catalogue available if Napster switches to a membership-only service.
Subscription service
Napster believes it can pay the record companies with the subscription revenues it will be receiving from July this year.
The new monthly subscriptions will range from $2.95 to $9.95.
Subscribers paying between $2.95 and $4.95 a month would be able to download a limited number of songs. Those paying $9.95 would have access to an unlimited number of songs.
Users will be asked to pay more money to burn CDs and to transfer their music to portable devices.
Napster's plan may yet falter, if its millions of users are reluctant to pay for a service they have so far been able to use for free.
However, Napster's Hank Barry estimates that in the first year, five million paying users would generate $297m in revenue.
"Napster has a viable business model with solid revenue streams and we are building the technology to make it happen," he said.
Traded files
Current Napster software allows users to search for MP3 music files stored on the hard drives of potentially millions of users. The files can be swapped for no charge.
The company says its $1bn offer to the music industry is based on the number of files traded over its service.
"We all ought to sit down and settle this case as fast as we can," said Napster chief executive, Hank Barry.
"We're saying this is something consumers really want. Let's do something to keep it going."
But the president of the Recording Industry Association of America (RIAA), Hilary Rosen, said the online company should accept the federal injunction ordering it to block copyrighted music from its service.
'Not enough'
"This path would be more productive than trying to engage in business negotiations through the media," said Ms Rosen.
"Stop the infringements, stop the delay tactics in court, and redouble your efforts to build a legitimate system."
Observers said Napster's settlement proposal does not even come close to the money the record companies believe they are owed for copyright.
So far only Bertelsmann, which has a strategic alliance with Napster, has come out in favour of the proposed settlement.