WASHINGTON—The White House is discussing easing social-distancing guidelines as early as next week as advisers and business leaders push President Trump to boost an economy beset by deepening job losses nationwide, people familiar with the discussions said.

The president has told people that he wants to open the economy as soon as possible. The talks have centered on relaxing or restructuring the 15-day guidelines the administration issued last week to stem the spread of coronavirus, one of the people said. Other advisers...