Best Buy is moving into a position to take a piece of the market share for music downloads. The electronics retail giant’s bid Monday to acquire online music provider Napster would continue Best Buy’s quest for mobile dominance by boosting its mobile music offering, while attempting to rescue the struggling Napster in the process.

Minneapolis-based Best Buy on Monday said it has entered into a merger agreement with Napster to acquire the once-illegal, now-legit music service for a total of $121 million. The Napster purchase comes on the heels of Best Buy opening Best Buy Mobile stores in its 970 United States retail last month. Best Buy Mobile, which is essentially a store-within-a-store offering mobile phones and devices, plans and accessories, was part of a two-year conversion for Best Buy.

Best Buy also recently became the first retailer outside of Apple and AT&T stores to sell the coveted Apple iPhone 3G.

While Best Buy already has a working partnership with Apple, the Napster buy would help it to better compete with Apple’s iPod and Apple’s iTunes music service, which currently holds a roughly 70 percent stake of the digital music market. The Napster deal will also pit Best Buy in stronger competition with Amazon, which recently added the digital music offering Amazon MP3 to its portfolio.