The move would fulfill a pledge Obama made during the presidential campaign and could signal a new openness with the communist nation.
The Wall Street Journal first reported the development on Friday.
Democrats in Congress are also moving to loosen restrictions on family travel to Cuba, but Obama plans to use presidential powers to ease the rules on his own.
The president does not intend to call for lifting the decades-long trade embargo against Cuba, which would require congressional approval, the newspaper report said.
During the presidential campaign, Obama pledged to allow unlimited family travel and remittances to Cuba. "It's time to let Cuban-Americans see their mothers and fathers, their sisters and their brothers," he said in a speech last May in Miami. "It's time to let Cuban-American money make their families less dependent on the Castro regime."
The rules will affect an estimated 1.5 million Americans who have relatives in Cuba, the Journal said.
---
Associated Press writers Jennifer Loven and Mark S. Smith contributed to this story from Strasbourg, France.