The Times said the deal tentatively included Nickelodeon, MTV, Comedy Central and other popular Viacom channels.
Viacom operates more than 20 channels, the Times said.
The deal allows Sony, which is creating its own Internet service, to offer real-time programming for subscribers. The service would be similar to Hulu and Netflix, which have vast libraries of programming that consumers download.
The source requested anonymity because the companies had not made a public announcement, the Times said.
Industry analysts said the Sony-Viacom deal could open up many more options for customers, who currently require either a cable service or a satellite service for television broadcasts.
That doesn't mean television is poised for a radical make-over, one analyst said.
"I don't think the classic pay TV subscription bundle model of television is going away anytime soon. It's a pretty compelling and cost-efficient smorgasbord," said Tim Hanlon, who runs the media advisory firm Vertere.
"But all bets are off with the under-40 set -- the growing group of folks who just want their video content when and where they want it, preferably without the messy commitment part," Hanlon said.