Treasury Secretary Timothy Geithner has told President Barack Obama that he is considering stepping down soon after policy makers agree to raise the government's borrowing limit, a person familiar with the matter said.

No decision has been made and Mr. Obama could ask Mr. Geithner to stay. But Mr. Geithner's family is moving to New York from Washington in coming months and he is expected to join them, and he has mused publicly and privately in recent weeks about leaving Treasury.

He...