Scott Sheffield, CEO of Pioneer Natural Resources. Adam Jeffery | CNBC

Chevron's $33 billion deal to buy Anadarko Petroleum is having a halo effect for U.S. oil drillers, as investors place bets on the next acquisition target in the U.S. shale oil space. Shares of drillers with positions in the Permian Basin are on the rise following the deal, the sixth biggest on record in the oil and gas sector by enterprise value.

The Permian Basin, which stretches across western Texas and southeastern New Mexico, is the center of a renaissance in U.S. oil and gas drilling. Chevron's tie-up with Anadarko isn't just about stitching together their Permian acreage, but the opportunity was a driving force in the deal. Many of the shale space's biggest gainers since the deal are drillers that focus exclusively on the Permian.

Paul Sankey, oil equity analyst at Mizuho Securities, said that makes sense. He believes future consolidation will be driven by efforts to more efficiently develop Permian acreage. Drillers can do that by stringing together big strips of land that make it more cost-effective to execute the advanced drilling methods necessary to extract oil from shale rock formations. Following the deal, Chevron boasted that the combined company would have a 75-mile-wide corridor in a sweet spot of the Permian. "As a consequence, expect focus to be on complementary acreage position, which helps explain the recent performance of the Permian pure-plays following the CVX-APC news — a single basin operator seems a lot simpler to integrate into an existing position," Sankey said in research note Wednesday. CNBC's Jim Cramer thinks that the company most likely to get a bid is Pioneer Natural Resources, a driller led by Scott Sheffield that recently shed assets to become a pure-play Permian producer.

"That's the one that I think gives you very good Permian. Scott is a very shareholder-conscious gentleman," Cramer said Monday. He noted that Pioneer's $29 billion market capitalization is in the ballpark of Anadarko's stock market valuation. Still, analysts aren't ruling out mergers and acquisitions of large Permian players and more diversified drillers with Permian acreage. Some of the candidates include Occidental Petroleum and EOG Resources, Ion Energy Group consultant Kyle Cooper told CNBC's "Closing Bell" last week. Cramer believes both Occidental and Exxon Mobil need to do a deal in the wake of the Anadarko buyout. Despite offering a higher price for Anadarko, Occidental lost out to Chevron, sources told CNBC's David Faber. According to Sankey, Occidental is the clear loser in the deal. He believes Occidental could now approach the likes of ConocoPhillips about a merger.