One of the tech giant executives Jimmy Iovine - also a producer and label boss - said it was only a matter of time before the Silicon Valley company would stop selling songs, the BBC reported.
Although stating there was no timescale as to when iTunes would cease to be made available for users, Iovine said: "If I'm honest, it's when people stop buying. It's very simple."
Apple is currently competing against Spotify for domination of the music subscription market and analyst at MIDiA Research, Mark Mulligan, predicted iTunes will be closed by 2020.
He said: "Apple will turn off its download store at some point.
"At some stage in the future, Apple having an iTunes music store will be as incongruous as Currys selling black and white TVs."
Currently Spotify is the world's largest music service, with around 70 million subscribers, but Apple's subscriptions continue to grow and experts believe it will be the top site at the end of 2018.
The mobile phone company recently revealed they are developing a new product with the capability to bend in the middle, according to a top expert, and the phone is nearly ready to launch, the Sun Online reported.
Apple first released their popular iPhone back in 2007 and over the years, the development of the needed technology hasn't really changed much - with phone makers sticking to the slim, rectangular design.
This news comes after Apple revealed they are planning to launch a new colour variant of the iPhone X in an attempt to restore sales.
Currently the device is available in tow colours - space gray and silver - compared to the other phones which offer more colour availability.
The iPhone X has seen poor sales since its first release due to the price of the product and Apple are reportedly working on ways to boost their original poor sales.