The National Basketball Association is seeking to double the TV-rights fees it receives from ESPN majority owner Walt Disney Co. and Time Warner Inc. 's Turner Broadcasting, as the league looks to lock up deals for nationally televised games in the coming months, according to people familiar with the matter.

Disney and Turner have eight-year contracts in place that run through the 2015-2016 season, but the companies are already in preliminary discussions with the league about extending their deals. Disney is currently paying about $485 million a year, while Turner's deal is worth $445 million a year. Given those terms, doubling the payments implies the new deals would be worth a total of nearly $15 billion for the NBA, assuming the length of the new deals remains eight years.

NBA team owners are meeting Tuesday to discuss TV-rights deals and other matters.

In a twist, the NBA may look to split up the NBA Finals between the two media companies, so that the championship round games would air on channels belonging to both, the people familiar with the matter said. That could take various forms: The networks could alternate Finals coverage each year, or carve up the Finals—played as the best-of-seven—in a given year.

Currently, the Finals air entirely on Disney's ABC broadcast network, but Turner is pushing to get a piece of the coverage, the people said. Disney wants to maintain sole rights to the Finals, and the NBA can't offer up those rights to anyone else in the short term without Disney's consent, one person familiar with the matter said. The league could only do so if it fails to reach a new deal with Disney, a process that could stretch well into next year, the person said.