The sources, speaking to Digital Music News, said users would be given "ample warning" of the upcoming phase-out.
The source also stressed that existing music downloads will always work on all Apple devices and the iTunes platform.
An Apple Music executive has previously confirmed that music downloads would be terminated, although an exact date wasn't given.
"If I'm honest, it's when people stop buying," the executive, Jimmy Iovine, told the BBC. "It's very simple."
Last month, an internal e-mail, titled "The End of iTunes LPs" was leaked to the Metro.
The email was sent two weeks ago from an address at "The iTunes Store," and was signed by "The Apple Music Team."
The email said that "Apple will no longer accept new submissions of iTunes LPs after March 2018.
"Existing LPs will be deprecated from the store during the remainder of 2018.
"Customers who have previously purchased an album containing an iTunes LP will still be able to download the additional content using iTunes Match", the email read.
The anonymous source who leaked the email to Metro told the publication: "It's clear that streaming is the future. Apple wants to push people to take out subscriptions."
While Metro reported that LPs would be removed from iTunes, Apple confirmed to tech site The Verge that existing LPs will continue to be available.
At the time, Mark Mulligan, an analyst at MIDiA Research and music industry blogger, told the Metro that the announcement was "potential evidence" of Apple's future plans.
"This could show Apple will turn off its download store at some point," he said.
"At some stage in the future, Apple having an iTunes music store will be as incongruous as Currys selling black and white TVs."
