An article from the New York Times is referencing sources claiming that EA has approached Valve a number of times in an attempt to purchase the company. Valve, however, has not been receptive to the idea. They instead prefer to remain under the ownership of Gabe Newell, who created the company in 1996 with then partner Mike Harrington. In the same article Newell provided the comment that he would rather the company "disintegrate" before it sells.
"It’s way more likely we would head in that direction than say, ‘Let’s find some giant company that wants to cash us out and wait two or three years to have our employment agreements terminate."
As a privately held company, Valve is able to do many things differently than your typical developer, for example the upcoming Big Picture experiment or the Dota 2 tournament The International, which had a $1,000,000 prize for the first place team -- provided entirely by Valve. These are just a few examples of Valve's willingness and interest in doing more than be a game developer/platform developer.
Which is of course a good reason for any large company, like EA, to be interested in purchasing Valve. While Valve is certainly valuable simply due to its existing game titles and the Steam platform, its true worth is in what's ahead. Sequels or new franchises, expansion into hardware or non-gaming software, and who knows what else. It's a future worth protecting, a future Gabe Newell isn't willing to pass off to the public or anyone else.