The Kindle Fire has just barely reached the market, but all eyes are already on what Amazon.com (Nasdaq: AMZN) may have in store next.

The readily apparent theme of the first Kindle Fire's iFixit teardown was that Texas Instruments (NYSE: TXN) was the big winner as a supplier of numerous bits and pieces. The device shares a lot of innards with the Research In Motion (Nasdaq: RIMM) PlayBook since both are assembled by third-party manufacturer Quanta.

There's a lot of consensus that the Kindle Fire 2, codenamed "Hollywood," will feature a larger screen that may compete more directly with Apple's (Nasdaq: AAPL) iPad, possibly as large as 10 inches. Boy Genius Report had exclusively reported earlier in the year that it would feature NVIDIA's (Nasdaq: NVDA) quad-core Tegra 3, according to its "tipster."

The latest hint that hopes to confirm that rumbling is a research note from Canaccord Genuity analyst Bobby Burleson, who cites "conversations with sources in the tablet supply chain." Burleson also pegs the screen size at 8.9 inches, up from the current 7-inch display. He also adds that "a win or loss in the next gen Fire could be seen as a proxy for [Texas Instruments'] overall apps processor potential in higher-end tablets."

There are really only two possible contenders here: NVIDIA and Qualcomm (Nasdaq: QCOM). The next-generation Kindle Fire -- can a Fool ponder if it will be called the Blaze or the Inferno? -- is thought to make an appearance as early as the first quarter of 2012 sporting a quad-core processor. That's a mere one to four months from now.

NVIDIA is the first ARM Holdings (Nasdaq: ARMH)-based chip maker to ship a quad-core mobile CPU, although Qualcomm has previously said its quad-core Snapdragons should be available to gadget makers by year's end and in consumers' hands in early 2012. Apple's next processor, presumably dubbed the A6, is expected to sport four cores, but good luck getting any official info out of Cupertino.

TI has all but ditched quad-core mobile chips amid doubts over cost and temperature. It wouldn't be surprising if it starts to lose mobile ground as a result of that decision, in line with Burleson's proxy statement above.

This rumor has some serious legs to stand on, and NVIDIA's mobile strategy is one reason I'm bullish on the chip maker. In all likelihood, the next-gen Kindle Fire is about to enter production ahead of an early 2012 launch.

Add Amazon.com and NVIDIA to your watchlist to keep up with the next Kindle Fire. Get access to this free report on the mobile revolution and why it's going to be huge.