Saudi Arabia is hunting for an energy deal in American shale country, as economic upheaval pushes it to seek its first international oil-and-gas production investments.

Saudi Arabian Oil Co., known as Aramco, has had initial conversations about either taking a stake in Tellurian Inc. TELL, -1.36% , a liquefied-natural-gas developer based in Houston, or agreeing to buy some of its fuel in the future, people familiar with the matter said. Separately, it has also inquired about acquiring assets in two giant U.S. oil and gas basins, the Permian and Eagle Ford, the people said.