Warren Buffett and Berkshire Hathaway (BRK.A 1.38%) (BRK.B 1.44%) spent much of 2013 looking for another "elephant" acquisition, which he failed to make. This got me to thinking, though: Throughout much of 2013, the Oracle of Omaha believed the market was in some places still undervalued. After recent declines, will Buffett make his move?

While it's impossible to know what Buffett will acquire next for sure, we can compile a list of possible candidates based on previous acquisitions.

What to look for
Indeed, we already know that Buffett has around $40 billion of cash at Berkshire. However, we also know that Buffett likes to keep $20 billion on hand to stay "liquid." Still, as with Heinz, Buffett is willing to partner up if the deal is good enough.

We also know that Buffett likes companies with a strong brand presence, like Heinz and Coca-Cola. What's more, we can assume that Buffett is unlikely to spend his cash on a company that relies on a commodity for its revenue.

So where does this leave us? Well, for the sake of simplicity, let's rule out companies that are based outside the U.S., as well as any companies worth less than $10 billion, as they're not true "elephants." Furthermore, we know Buffett is a value investor but is willing to pay a bit more for quality.

For example, he bought Heinz at an all-time high price and valuation. So let's narrow the search down to companies that are currently trading at a trailing-12-month price-to-earnings ratio of less than 20 -- not particularly cheap but not overly expensive, either.

Two possible candidates
Apply these screening criteria to the S&P 500 index, and two companies immediately stick out. Travelers (TRV 1.28%) and Chubb (NYSE: CB) would both make great bolt-on acquisitions for Berkshire and would greatly expand its presence within the domestic insurance market. Both companies have a strong brand and solid history and are in an industry that Buffett knows well.

And there's another reason why Buffett might target these companies. As you may know, a large portion of Berkshire's revenue comes from insurance, which is the company's main line of business. However, there are some problems plaguing the insurance market that are likely to affect Berkshire more than most.

Demand for yield
The demand for yield around the world has driven investors into ever more exotic areas in search of a steady income stream. One region that has seen significant capital inflows is the insurance market. One common focus is securities such as catastrophe bonds, which are designed to raise a large amount of capital in exchange for a higher-than-average rate of interest. Catastrophe bonds are high-risk, high-reward assets. They offer a high rate of interest, but in the event of a catastrophe, the issuer's obligation to pay interest and/or repay the principal is either deferred or completely forgiven.

The influx of capital and demand for these bonds has removed some of the demand for reinsurance companies, which previously took on this all-or-nothing style of investing. Berkshire Hathaway Reinsurance and General Re are the two main reinsurance operations under Buffett's wing. Together, these two companies accounted for 75% of the insurance float under Berkshire's control during 2012.

To explain further, here is an excerpt from Insurance Journal:

At present the only problem with capital is that there's too much. The capacity glut has lowered reinsurance rates, especially in property [catastrophe], and is making it more difficult for reinsurers to achieve a reasonable return on equity. An additional $100 billion will come into the reinsurance market in the near future. Finding ways to profitably invest that money, while avoiding unnecessary risks, is a huge challenge.

In addition, Evan Greenberg, CEO of ACE Limited (one of the world's largest reinsurance groups), said only last week that the firm was prepared to shed business in order to maintain profit in the softening market.

Unfortunately, this is bad news for Berkshire. However, this could be the catalyst that inspires Buffett to unleash his elephant gun on either Travelers or Chubb, as both companies are highly active in the personal-insurance market.

But why have I chosen Chubb and Travelers? For starters, it is widely speculated that Buffett already tried to acquire Chubb in a deal that fell through in November 2012. After the company's recent release of impressive fourth-quarter results and the approval of yet another $1.5 billion stock buyback, the Oracle could be drawn to the company once again.

What's more, analysts have consistently expressed belief the both Chubb and Travelers would make great Berkshire add-ons. In June of last year, according to the Bloomberg "Riskless Return Ranking" of insurance companies, Chubb and Travelers were the best-performing companies within the insurance sector. Both companies beat Berkshire.

In addition, both companies remained profitable throughout the financial crisis, and their stock prices have gained slowly and steadily during the past decade. This is what makes these two companies so appealing: They are both perfect fits to Buffett's low-risk, slow and steady methodology.

Foolish summary
While I can't say for sure what Berkshire will buy up next, trends within the insurance market and Berkshire's history lead me to believe the next acquisition could be within the insurance sector.

Travelers and Chubb both fit the bill, and both companies are currently within Buffett's price range. To me, both look like perfect bolt-on acquisitions for Berkshire.