Keeping these key personnel in place will ensure there are senior officials at all times authorized to carry out key functions in the event of an emergency, and that the military can operate smoothly immediately after the inauguration, two officials said.
A spokesman for the Trump transition declined to comment.
The Pentagon officials are being asked to stay until key Trump appointees can be confirmed by the Senate and take office. They could stay for up to three months, the first official said, but they also can leave at any time if they so choose.
The most senior official asked to stay on is Deputy Secretary Robert Work. He was asked specifically to temporarily extend his service by James Mattis, nominated to become secretary of defense. If Mattis for some reason is not sworn into office immediately upon Donald Trump's taking office, Work would be in place for any urgent development, even if it came in the minutes before Mattis is sworn in.
For example, should a senior Pentagon civilian be needed to authorize the shoot-down of a threatening aircraft or an emergency deployment of US troops, Work could step in as acting secretary of defense, the officials said.
While the scenario is unlikely, every effort is made to ensure the so-called continuity of government during transition periods, one senior Obama administration official told CNN.
Work also has extensive expertise in defense budgeting, research, development and acquisition issues and is expected to assist Mattis with that in the first weeks of the administration as a multibillion defense budget, crafted by the Obama administration, is sent to Congress.
Other officials being asked to stay on temporarily:
*Robert Speer as acting secretary of the Army. He currently serves as assistant secretary of the Army for financial management and as comptroller.
*Sean Stackley as acting secretary of the Navy. He currently serves as assistant secretary of the Navy for research, development and acquisition.
*Lisa Disbrow as acting secretary of the Air Force. She is the current undersecretary.
At the State Department, Brett McGurk, special envoy against ISIS, also will be staying on.
Deborah James, secretary of the Air Force, and Robert Scher, assistant secretary of defense for strategy, plans and capabilities, have also been asked to continue for now to work on special projects are. The officials did not have details on those projects.