While rival networks may be licking their chops in anticipation of trying to wrest away the media rights to the NBA, both legacy partners said they are confident that they’ll renew their respective contracts with the league.

Speaking to investors during his company’s fiscal year Q3 earnings call, Walt Disney Co. chairman and CEO Bob Iger said the NBA is a cornerstone of the ESPN lineup. “It’s certainly a priority of ESPN to extend their relationship with the league,” Iger said. “I think the league would believe that it would beneficial for them as well to stay on ESPN which is a very, very important platform for them.”

ESPN has had an active contract with the NBA since 2002. Its current deal, which runs through the 2015-16 season, is valued at $485 million per year.

“I don’t want to sound in any way as though we’re complacent, but I think it would be safe to assume that we’re reasonably confident that we will be able to extend that relationship,” Iger said. He went on to insist that he was not about to make any predictions on how much a new deal might cost Disney; nor would he speculate about what ESPN might do if the asking price is “substantially above what we expect.”

Along with college football and its Monday Night Football franchise, the NBA accounts for some of ESPN’s highest ratings. For example, during the 2011-12 season, ESPN was fortunate enough to carry the Eastern Conference Finals, a best-of-seven series between the Boston Celtics and Miami Heat. The deciding game drew a whopping 13.3 million viewers, or which more than half (7.14 million) were members of the adults 18-49 demo.

Unfortunately, ESPN ran into a bit of bum luck this summer, as its playoff matchups failed to provide much in the way of narrative tension. San Antonio blanked Memphis in four games in May, and then Miami beat the Chicago Bulls in five games to advance to the Eastern Conference Finals against the Indiana Pacers—a seven-game nail biter that aired on TNT. The end result: fewer games and lower ratings for ESPN.

For all that, ESPN sibling ABC Sports enjoyed a blockbuster NBA Finals, as the Heat and Spurs battled in front of a near-record crowd. Per Nielsen live-plus-same-day data, the series averaged 17.5 million viewers and a 7.1 rating; Game 7 was the second most-watched NBA game in ABC history, drawing 26.3 million viewers and a 10.6 in the demo. (Only Game 7 of the 2010 Lakers-Celtics title tilt delivered a bigger crowd, averaging 28.2 million viewers and an 11.4 in the 18-49 demo.)

The parent company of Turner Sports and NBA broadcast partner TNT on Wednesday echoed ESPN’s proclamation. Responding to an analyst’s query during Time Warner Inc.’s second quarter earnings call, CEO Jeff Bewkes said that he believes the NBA is in good hands with TNT.

“It’s one of the longest and strongest partnerships we have with any league,” Bewkes said. “We not only license the content but we manage both NBA TV and the NBA Digital properties for the league. We’re confident this relationship will continue, for many years to come.”

TNT’s contract with the NBA expires in June 2016, at which point both partners will have been paired up for 32 years. Turner pays $445 million per year for its rights package.

If recent blockbuster renewals with Major League Baseball and the NFL are any indication, ESPN and TNT can both expect to pay as much as double their current rates for a multi-year renewal. Low-ball it with a 75 percent annual increase and ESPN could wind up forking over as much as $850 million per year, while TNT could pay around $780 million per season.

Of course, rather than shut out Fox Sports 1 and/or NBC Sports Network altogether, the legacy partners could agree to carving out room for a third media rights holder. In any event, look for the negotiations to heat up shortly after NBA commissioner David Stern retires on Feb. 1, 2014.

Bewkes was a little cagey on the monetary question. “We all know that sports rights are going up, we feel pretty good about our position there and our ability to pay that and continue to have the earnings growth we’ve been showing you,” he said. “But we really don’t want to, obviously, say much more about it, because of course we’re talking about significant amounts of money. And I think you would want us to just go off and keep securing the programming that we judge it wise to have.”

Time Warner chief financial officer John Martin (soon to transition to the role of CEO of Turner Broadcasting System, Inc.) chimed in, noting that TNT and TBS are hybrid networks. “Sports is incredibly important, but our original programming is getting an increasing percentage of the schedule,” Marin said. “I think the NBA represents just 3 percent of our programming, in terms of overall hours. So, we have a lot of other programming that is extremely valuable to the affiliates and extremely valuable to consumers. … The NBA is important, but we’re going to be OK no matter what.”

Unlike ESPN, TNT enjoyed a particularly strong 2013 NBA Playoffs slate. Per Nielsen, the Turner net aired four of the top five June games, including the Indiana-Miami Eastern Conference Finals clincher that drew 11.6 million viewers and 6.44 million adults 18-49. TNT also hosted eight of the top 10 May playoff games and 15 of the top 20.

All told, this year’s playoffs were the third most-watched in the history of the NBA-TNT partnership.

Thanks in large part to an 11 percent boost in ad sales revenue, the Turner nets and HBO improved total Q2 revenue 7 percent to $3.84 billion.