Now, 11 years later, Jobs' successor looks poised to pay generously for a more evolved version of that service, and to bring on board Iovine into the bargain, betting that he can bring Apple some of the same creative flair that has made him a legend in the music business.
Iovine, CEO and co-founder of the Beats headphones and music streaming service Apple is close to buying for $3.2 billion, is best known as the co-founder of Interscope records, a rap music pioneer which has since branched out to include acts like Lady Gaga and U2.
If he does join Apple, the 61-year-old producer could lend a hand to CEO Tim Cook and try to bolster its subscription music services - which have yet to catch fire - as well as at iTunes, which has seen growth in downloads virtually evaporate.
A source familiar with the deal said Iovine would likely leave his record label and join Apple to run Beats, but it hasn't been determined if he would take on a greater role. It also isn't yet clear whether Beats would operate as an independent unit or to whom its executives would report.
After working as a sound engineer for artists such as Bruce Springsteen, Iovine in 1989 co-founded Interscope, which became one of the largest U.S. music labels. It took a bet on rap music that was controversial at the time, given the music's explicit lyrics. The political uproar eventually prompted Time Warner having to sell the label. It was bought by Universal Music Group, in 1995.
"He's one of these guys that bring intangibles," said Bill Werde, entrepreneur at Guggenheim Digital and former editorial director at Billboard magazine. "Sometimes you need a jolt of energy and Jimmy is certainly a guy who can provide that."
In a Jan 2013 interview with AllThingsD, Iovine said he pitched a subscription service to Apple's Jobs around 2003, but the Silicon Valley icon was not keen on it right away. Still, Iovine is said to be have been close to Jobs and helped him broker deals to co-market products such as a U2-branded iPod and music videos by the rapper 50 Cent holding an iPod.
Iovine founded Beats in 2006 with rapper Dr. Dre and its big, distinctive headphones found wide distribution, including in Apple stores. The brand launched a music streaming service earlier this year. It remains a fledgling venture although it has gotten attention for what some say is a unique ability to personalize music. Iovine met with Apple CEO Tim Cook in March 2013 to discuss the music service.
Iovine's music industry relationships will be valuable to Apple because they could make licensing for a future streaming service easier. The company's iTunes' revenue, which includes apps and books in addition to music, has decelerated, with growth dropping below 10 percent in the most recent quarter, according to BTIG Research.
In his own words, Iovine has said he has been "shocked at how culturally inept most consumer electronics companies are."
"Subscription needs a programmer," he told AllThingsD. "It needs culture. And tech guys can't do that. They don't even know who to hire. They're utilities."