Facebook founder and CEO Mark Zuckerberg is reportedly considering entering into the digital music business and becoming a streaming competitor to iTunes and MySpace.

Zuckerberg is in talks with several song streaming services and music community sites including Rhapsody.com, iMeem.com, iLike.com, and Lala.com, sources familiar with the situation said, according to the New York Post.

Facebook has had challenges in the past with the recording industry. In August 2007 it had to remove the third party application, Audio that allowed users to upload and stream music, after record labels complained of copyright violations. Working with a service like Rhapsody.com means that they would be above board with the labels immediately as Rhapsody would handle all of the billing and relationships.

Facebook’s entry into digital music would likely be different than MySpace Music, which is a joint venture between the four major record labels, Universal Music Group, Sony BMG, Warner Music Group and EMI.

The company does not want to get involved in trying to secure its own licenses to distribute music or build a proprietary service from the ground up.

Sources familiar with the talks cautioned that nothing is concrete, and Facebook could completely shelve its music plans altogether.

Facebook has been considering digital music off and on for about a year and when MySpace launched its music service, Zuckerberg’s interest in the idea is said to have increased.

The company has not commented on its music plans, but a Facebook spokesman said in a statement that “music sharing plays a part” in the site’s mission and that it is “always talking with potential partners.”