When Google unveiled its new music-specific search results last month, many digital music industry insiders wondered whether the search engine giant would stop there or go the next logical step: rolling out an iTunes competitor of its own.

Prominent Wall Street outfit Bear Stearns predicted the latter today, issuing a client note maintaining its "outperform" rating on Google and saying the company is looking to expand into the MP3 downloading business.

"We believe that Google is in the midst of creating its own iTunes competitor, which we've dubbed 'Google Tunes,'" analyst Robert Peck wrote in a client note issued today. "We think this is a logical step, now that the nascent Google Video product has been introduced."

Peck opined that a Google move into the music-download space made sense given its recent launch of its Google Video service. He also pointed out recent data that showed the explosive growth of unique visitors to the Web site of iTunes, easily the most dominant digital music store in the business with at least an 80 percent market share.

"Further, Nielsen [Net Ratings] indicates that iTunes users form a distinct target audience with brand preferences along autos, alcohol beverages, magazines, and television," Peck wrote.

"We would expect Google to roll out a Beta [music] service within three to six months," he continued. "We note that Google has not confirmed our expectations, and that our thinking is based on Mosaic theory. However, we do think this fits with Google's recent moves and its ultimate goal of organizing the world's information."

Google is set to report fourth-quarter earnings next Tuesday.