Will the fastest-growing social network buy the fastest-growing micro-blogging site? It would seem to be a killer combination. But the two sides can't agree on such a deal, just yet.

Twitter turned down an acquisition offer from Facebook of $500 million in stock, at the inflated $15 billion valuation it once pulled off. If Facebook offered cash it would certainly be a different story.

Apparently both sides were discussing a deal three weeks ago, reported Kara Swisher, of AllThingsD. Here are the reasons a deal fell through.

-The Twitter team felt Facebook's current valuation was inflated, establishing a value of $150 million for Twitter at the offer. Twitter was valued at $98 million in the last round

-The Twitter team believed Facebook's value should be more in the range of $5 billion

-The Twitter team wanted cash

-Facebook has to assume costly SMS fees, and Twitter lacks a revenue model to pay for them

(See my interview with former CEO Jack Dorsey about how he thought Twitter should make money) 

-Facebook may have to assume an SMS fee of up to $75 million, if Twitter were offered to Facebook’s 120 million users, Facebook execs estimate 

-The Twitter team believes it should take a shot at building a business

Here's more from Swisher:  

While some sources at Facebook said [Mark] Zuckerberg was becoming frustrated by the buzz Twitter was getting–a market that should have been dominated by Facebook–others at the company said he was interested in buying Twitter because of his respect for its progress.

Indeed, at the Web 2.0 interview, Zuckerberg called Twitter an “elegant model” and that he was “really impressed by what they’ve done.” Indeed, with about six million registrations, as reported in October, up 600 percent over the last year, the San Francisco-based Twitter–launched in 2006–has had impressive growth.