WASHINGTON—The government is considering enlarging the National Security Agency's controversial collection of Americans' phone records—an unintended consequence of lawsuits seeking to stop the surveillance program, according to officials.

A number of government lawyers involved in lawsuits over the NSA phone-records program believe federal-court rules on preserving evidence related to lawsuits require the agency to stop routinely destroying older phone records, according to people familiar with the discussions. As a result,...