The Trump administration’s new push for more federal detention facilities for immigrants awaiting asylum hearings or deportation has brightened the outlook for the country’s two largest private prison operators.

Tennessee-based CoreCivic Inc. and Florida-based Geo Group had already been helped by higher federal spending on Immigration and Customs Enforcement. Now, the Trump administration is seeking $2.8 billion in the 2019 budget year to increase the number of beds in immigration detention centers to 52,000—49,500 adult...