However, White House officials say a final decision has not been made.
In tapping McDonough, Obama would be relying on an inner circle ally for the key West Wing post. McDonough, 43, currently serves as the president's deputy national security adviser and is highly regarded by Obama and White House staffers.
McDonough would replace current White House chief of staff Jack Lew, the president's nominee for treasury secretary.
The people familiar with the White House thinking spoke on condition of anonymity because there has been no announcement an appointment.
Before his tenure in the White House, McDonough served as Obama's main adviser on foreign policy issues during the 2008 presidential campaign. Earlier, he worked as a foreign policy specialist in Congress, including as a senior foreign policy adviser to former Senate Majority Leader Tom Daschle, D-S.D.
McDonough would be Obama's fifth chief of staff. Rahm Emanuel, William Daly and Pete Rouse, as interim chief of staff, preceded Lew in the job.
If Obama chooses McDonough it will likely be less because of his national security credentials and more because of McDonough's highly regarded status within the White House.
"He's easy to work with and focused on getting the job done for the boss, hammering out the best policy possible given the political realities," said Doug Hattaway, a Democratic consultant who worked with McDonough in the Senate.
McDonough's place in Obama's inner circle was illustrated during the Navy SEAL raid that killed Osama bin Laden in May 2011. He is among those captured in a White House photograph seated in the situation room with Obama and other senior officials watching the raid unfold.
McDonough grew up in Minnesota, one of 11 children. Two of his brothers are priests. He is a graduate of St. John's University in Minnesota and received his master's degree from Georgetown University.
Associated Press writer Jim Kuhnhenn contributed to this report.