Mattis met with Trump on Nov. 19, and Kelly met with him the following day. The retired officers have long been colleagues and friends, with Mattis serving as a two-star general in charge of the 1st Marine Division during the 2003 invasion of Iraq and Kelly serving as his one-star assistant commander. They also have long personal and professional relationships with Marine Gen. Joseph F. Dunford, who commanded the 5th Marine Regiment under Mattis during the invasion and is now chairman of the Joint Chiefs of Staff.

Kelly and Mattis both declined to comment on their meetings with the president-elect, and spokesmen for Trump did not respond to a request for comment. But the source, who spoke on the condition of anonymity because of the sensitivity of the presidential transition effort, said that both generals found their conversations with Trump respectful and wide-ranging.

Trump’s interest in tapping retired senior officers for Cabinet positions has prompted some concerns that the military may wield too much influence in his administration. If Trump selects either man to serve as secretary of defense, it will require legislation to overcome a federal law that requires any retired service member to be out of uniform for seven years before becoming secretary of defense.

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Mattis oversaw operations across the Middle East as chief of U.S. Central Command before retiring in 2013. Like Trump, he has criticized the Obama administration’s stance toward Iran and has called for a more skeptical view of Tehran’s intentions and influence in the Middle East.