Liberty Media (NASDAQ:FWONA) CEO Greg Maffei reportedly made at least an informal offer to buy music streamer Pandora Media (NYSE:P) recently, raising speculation that the Liberty exec is looking to combine Pandora with satellite-radio service Sirius XM Holdings (NASDAQ:SIRI).

Although the offer for $15 a share was reportedly rejected -- with Pandora allegedly seeking somewhere around $20 a share -- it raises questions about the future of the satellite service, its biggest shareholder, and how streaming may fit into the mix.

Liberty owns a 64% stake in Sirius XM, and although it's been hands-off in Sirius' operational matters so far, the reported moves toward Pandora would seem to indicate that the company might be willing to step in if it sees the right opportunity.

But would combining Pandora and Sirius make sense? From the perspective of adding an instant streaming audience and established streaming app to Sirius XM, yes. But from other angles, the two services seem like a mismatch that would be bound for trouble.

Here's why the deal might seem to make sense

Satellite radio was disruptive, cutting-edge technology a decade ago, when Sirius and XM were battling for customers and began considering a merger. But the satellite technology that allows it to deliver audio programming to your car, wherever you are, quickly lost its place on the bleeding edge, as smartphones became smarter and more powerful, and streaming services put music at every potential listener's fingertips.

Many saw that as the beginning of the end for Sirius XM and calls for the company to acquire a streaming service or develop its own have been surfacing over and over again ever since.

An acquisition of Pandora would deliver Sirius XM one of the biggest names in streaming, along with its nearly 80 million listeners. It would also deliver about $1.4 billion in annual revenue, a tidy boost to Sirius XM's expected $5 billion 2016 revenue.

But there would be problems with such a marriage.

It's a business-model mismatch

Sirius XM executives have been exploring the possibility of acquiring a streamer for years, and they haven't seemed to warm up to the idea. That's in part because the streamers have yet to pose a significant threat to Sirius XM's subscriber growth, which continues to tick along, up 8% in the first quarter. A few years back, the rise of the streamers looked like the end of the line for Sirius.

But perhaps the more important reason for investors to be wary of any proposed Sirius XM/Pandora merger is that these companies have very different business models.

Sirius generates some 84% of its revenue from subscriptions.That's reliable, predicable cash flow for the company, which has been using that money to increase shareholder value through buybacks and has recently talked about a potential dividend. Sirius XM's subscription-based business model generated $1.3 billion in free cash flow last year, and it should be able to continue spinning off a lot of cash now that most of its major capital expenses from its satellite system are behind it.

Just 3% of Sirius XM's revenue comes from advertisements, and even though that is the fastest-growing area of its business, it's not one it's counting on to grow to more than 10%.

Pandora, meanwhile, relies on ads for 77% of its overall revenue and Pandora's ad business is struggling. The streamer's second-quarter ad revenue was up just 15% year over year. That's slower growth than Sirius XM's advertising business has seen. Ad revenue for the satellite-radio company was up 17% last quarter.

So while Sirius XM's business model may be prone to disruption as streamers build better services, Pandora operates in a much more turbulent arena, competing for ads with digital giants such as Alphabet and Facebook.

So, from a business-model perspective, it doesn't make a lot of sense for the company to acquire a music streamer generating negative cash flow and showing slowing growth in listeners and revenue generation, especially when Sirius XM executives say the streamers haven't disrupted their business to any material degree.

If this all a big head fake?

But there might be another explanation for why Maffei would have made an offer for Pandora This comes via BTIG Research's Brandon Ross: "It is possible that Liberty actually is not interested. Perhaps [Liberty CEO] Maffei is simply toying with Sirius's competitors, hoping to ensure someone overpays for Pandora, assuming it ever finds a buyer."

To be fair, Ross goes on to say he believes there is some genuine interest on Liberty's part and that this isn't all just gamesmanship. But his conjecture highlights the skepticism about any real benefits of a Pandora-Sirius marriage.

By buying Pandora and looking to combine it with Sirius, Liberty would essentially be forcing the satellite-radio company into a shotgun wedding. Those don't usually end well.

This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.