The pair had previously set the idea up as a film project for Sony, but Murphy now plans to pitch to cable networks later this year.
The anthology series would see Paltrow star in the first season before new castmembers join future runs, The Hollywood Reporter said.
Murphy said that "One Hit Wonder" would see Paltrow as a broke singer who had a hit 15 years previously. At her lowest ebb she is contacted by a record label looking to form a supergroup with three other singers from her era who are equally hard on their luck.
Reese Witherspoon and Cameron Diaz were previously linked to star alongside Paltrow in the movie version before it was cancelled.
Paltrow has shown off her musical prowess before, most notably in the 2010 movie Country Strong alongside Tim McGraw. She also starred in a number of episodes of "Glee" as substitute teacher Holly Holliday.