According to Deadline, Amazon is the company that has been secretly developing the Wheel of Time TV series alongside Sony for the last few months.
Amazon had previously been strongly linked to the Wheel of Time deal prior to their acquisition of the Lord of the Rings TV prequel rights. It was assumed that Amazon would not be interested in developing two epic fantasy shows simultaneously. Since then, they've also announced that they are developing a Conan the Barbarian TV project and are moving forwards with TV adaptations of Larry Niven's Ringworld, Neal Stephenson's Snow Crash and Iain M. Banks' Consider Phlebas. Amazon are not short of money and the company's owner, Jeff Bezos, is a known SFF fan with very, very deep pockets.
Recently there has been forwards movement on the project: the Sony-appointed showrunner Rafe Judkins has tweeted he is in full writing mode on the script and producers Radar Pictures have been gearing up for an announcement (the massive success of their movie Jumanji: Welcome to the Jungle meaning that some of their other projects are moving forwards).
A formal confirmation of the news is still awaited, although at this point Amazon is considered the front-runner for developing the series (with the small possibility of Apple TV, CBS All Access or maybe the new Disney streaming service sweeping it up) and it'd be surprising if it went anywhere else.