Shares of Napster surged more than 30 percent in premarket trading on news of the report.
Napster told Reuters last week that it was not on the block. "The company is not looking to be sold, the management is not looking to step out. It's simply not true," a Napster spokesman said on Jan. 23.
Also last week, Napster, founded by college student Shawn Fanning and once synonymous with the pirating of music,.
Some 355 online music sellers exist globally, according to a report by the International Federation of the Phonographic Industry, with a shakeout in the industry largely expected, digital music industry executives have said.
Google has been in discussions with Napster to offer a digital music service, rather than start one on its own, the Post reported.
Napster shares rose $1, or 32.05 percent, to $4.12 in premarket trading, from a close of $3.12 on the Nasdaq on Monday.
Google shares rose 75 cents to $427.57 in premarket trading from a close Monday of $426.82 on the Nasdaq.