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(CNN Business) —  

Investing legend Warren Buffett is looking for an “elephant” of a deal to help Berkshire Hathaway’s portfolio fly higher.

The Oracle of Omaha wrote in his latest annual shareholder letter in February that he’s itching to make a sizable acquisition .

Buffett conceded that the likelihood of an imminent deal is remote because the stock market rally has made most takeover targets prohibitively expensive.

“Prices are sky-high for businesses possessing decent long-term prospects,” he wrote, adding that this “disappointing reality” will likely mean that Berkshire will add to its pile of cash.

“We continue, nevertheless, to hope for an elephant-sized acquisition,” Buffett said.

The company’s last major deal was the purchase of aerospace parts maker Precision Castparts for $37 billion in 2015.

Berkshire-backed Kraft Heinz (KHC) tried to buy Unilever (UL) in 2017 but the Anglo-Dutch maker of Dove soap, Lipton tea and Ben & Jerry’s ice cream, turned down the offer.

And Buffett told CNBC in February that he was close to doing a big deal in the fourth quarter of last year but that the acquisition fell through for unspecified reasons.

With all that in mind, investors will probably ask Buffett and Berkshire Hathaway vice chairman Charlie Munger about possible deals at the company’ s annual shareholder meeting in Nebraska in May.

Itching for a major acquisition

Trip Miller, founder of hedge fund Gullane Capital Partners and a Berkshire Hathaway shareholder, said that the company’s more than $110 billion in cash and marketable securities is “a wonderful problem to have.”

Miller thinks Berkshire Hathaway is probably looking to do a major deal.

“For a gun that big, I would think an acquisition would be, at a minimum, $25 billion,” Miller said.

Miller said FedEx (FDX) could make sense, given Buffett’s love for transportation stocks. Berkshire Hathaway already owns railroad Burlington Northern Santa Fe and has stakes in airlines Southwest (LUV), Delta (DAL), American (AAL) and United (UAL).

“This is the kind of thing Buffett looks for,” Miller said. Gullane Capital owns a stake in FedEx.

Miller added that discount retailer Dollar General (DG), which is also in Gullane Capital’s portfolio, could be another good fit for Berkshire, given Buffett’s ownership of brand name consumer companies such as catalog retailer Oriental Trading, Dairy Queen, Duracell and Fruit of the Loom.

Don’t rule out Berkshire buying a big airline

But what about airlines? Southwest and Delta have both been the subject of vague Berkshire Hathaway takeover rumors lately.

Miller was skeptical, noting that Berkshire already owns many shares of the four leading carriers.

Still, there is precedence for Berkshire Hathaway picking just one company in an industry to acquire.

When Berkshire Hathaway announced the Burlington Northern Santa Fe deal in 2009, it also had investments in BNSF rivals Union Pacific and Norfolk Southern. Berkshire Hathaway wound up selling those stakes.