In at least some of the talks, Amazon has proposed a premium, exclusive sports package as part of its Amazon Prime subscription service, sources told the Journal. The U.S. online retailer has even looked to foreign sports like cricket, and has asked traditional broadcasters like Disney and Univision for rights to games they choose not to air.
A source close to the situation confirmed to CNBC that Amazon has been interested in sports, particularly the NFL, for some time, and said that Amazon bid on the rights to games that ultimately were streamed by Yahoo and Twitter.
Disney, the parent company of ESPN, saw shares fall 0.6 percent on Monday, while Amazon shares closed 2.6 percent higher. CNBC has reached out to Disney and Amazon for comment. The NFL declined to comment.
Amazon announced aggressive plans earlier this year to build out its video content platform, saying it would double its video content spending and triple its spending on original content in the second half of 2016. Amazon joins fellow tech titans like Twitter and Facebook, who have also looked to sports to bolster their video offerings this year.
But these companies may face a challenge, since many broadcasters already have long-term deals to air the games, the Journal reported.
—CNBC's Julia Boorstin and Mike Newberg contributed to this report.
Disclosure: CNBC's parent company, NBCUniversal, also owns NBC, which broadcasts sports like NFL games.