Well, that's a surprising nugget of news. According to Bloomberg, Western Digital offered to purchase Seagate shortly after the latter confirmed, in mid-October, that it was in talks to sell itself and go private. Bloomberg's sources say Seagate ended up turning down offers from both WD and private equity firm TPG Capital.
Western Digital was reportedly willing to put up quite a bit of money: "10 percent to 50 percent" more than TPG, which is itself reported to have bid more than $7.5 billion. That's way more than what WD has kicking in the bank ($2.9 billion, Bloomberg says) and more than the company itself is worth on the stock market (about $8 billion). That said, the talks apparently didn't break down because of financial reasons. Bloomberg quotes its sources as saying a WD-Seagate merger "would have faced antitrust obstacles and may have resulted in management departures."
As an analyst quoted in the story points out, there's quite a bit of overlap between the two companies' product offerings—you know, since they're direct competitors and all. This wouldn't have been like AMD's 2006 buyout of ATI, where the two parties were clearly complementary, and the deal gave AMD a strong chipset business and the ability to integrate graphics into its CPUs. More likely, it would have resembled Seagate's takeover of Maxtor, in which the goal was to eliminate a competitor and consolidate market share.