The Huffington Post reported late last month that Klein, who oversees the Post's Wonkblog, was speaking to "outside suitors about starting a new media venture," but was still in talks to stay with the newspaper.
But the New York Times indicated Thursday that Klein's future with the Post is even more doubtful now.
Klein's proposal to the Post, according to the Times, was a semi-autonomous "website dedicated to explanatory journalism on a wide range of topics beyond political policy." He reportedly sought an eight-figure investment, but failed to win support from the Post.
Klein, who joined the newspaper at the age of 24, also serves as a contributor to MSNBC.