Hasbro sells Scrabble in North America and Mattel markets it in other parts of the world.
The companies said the online game Scrabulous was piracy and threatened to take legal action against software development company operators Rajat and Jayant Agarwalla, The New York Times reported Sunday.
The companies said they hoped the solution would not include shutting down the game, which has attracted more than 700,000 players, the Times reported.
"People believe it to be in the public domain, like chess. The idea that Scrabble belongs to a corporation is something that people don't or are unwilling to accept," National Scrabble Association Executive Director John D. Williams Jr.
The Agarwalla brothers reportedly said they did not intend to make a profit from their online game, but now they receive approximately $25,000 each month from advertising.