Those believed to be under consideration include Marine General John Kelly; Fran Townsend, and Congressman Michael McCaul
He was the second retired general to be picked for the cabinet after lieutenant general Mike Flynn, Trump's choice as national security adviser.
The following is a list of key nominations made by Trump so far:
Attorney General: Jeff Sessions, 69
One of Trump's earliest supporters during the campaign, the anti-immigration senator from Alabama has a much criticized record on race relations and was once denied a judgeship amid concerns over past comments about blacks.
CIA Director: Mike Pompeo, 52
A strident critic of the Iran nuclear deal, the hawkish Kansas congressman was elected in 2010 to the House of Representatives, where he was a member of the hardline Tea Party faction and one of the leaders of the controversial Benghazi Committee that targeted Trump's Democratic presidential rival Hillary Clinton.
Commerce: Wilbur Ross, 79
A US asset investor and billionaire, Ross is best known for investing in failing steel and coal firms and selling them for profit. He was once known as the "king of bankruptcy" for his history of investing in such businesses.
Defense Secretary: James Mattis, 66
A retired four star Marine general, Mattis commanded US forces in the Middle East and Southwest Asia from 2010 to 2013, capping a career as a combat commander that earned him the nickname "Mad Dog." A scholar of warfare, he is said to have a particular interest in the challenge posed by Iran. He opposes the use of torture, bluntly telling Trump in their first interview he could do better with a pack of cigarettes and a couple of beers. To become secretary of defense, Mattis would have to get a congressional waiver from a law that bars generals from serving as defense secretary for seven years after leaving active duty.
Education: Betsy DeVos, 58
A wealthy activist and Republican megadonor from Michigan, DeVos is a champion of alternatives to local government schools, a movement that advocates the use of tax credits and vouchers to allow parents to opt out of the public school system.
Health and Human Services: Tom Price, 62
The Georgia lawmaker and former orthopedic surgeon is a robust critic of President Barack Obama's signature health care reform law, the Affordable Care Act, which has provided health coverage to 20 million Americans.
National Security Advisor: Retired Lieutenant General Michael Flynn, 57
A top military counsel to Trump, the retired three-star general, a veteran of America's wars in Iraq and Afghanistan, has courted controversy with extreme statements that critics say border on Islamophobia, but has taken a more flexible line on Russia and China.
Transportation: Elaine Chao, 63
The Taiwan-born former US labor secretary under president George W. Bush also served as the deputy secretary of transportation in his administration. She was the first Asian-American woman to serve in the cabinet and is the wife of Senate Majority Leader Mitch McConnell.
Treasury: Steven Mnuchin, 53
The Wall Street veteran was a partner at Goldman Sachs before he launched an investment fund backed by Democratic Party supporter George Soros and financed Hollywood blockbusters like "Avatar" and "Suicide Squad."
Ambassador to the UN: Nikki Haley, 44
As South Carolina's governor, Haley rose to prominence when she led efforts for the divisive Confederate flag to be pulled from the state's capitol following a 2015 massacre at a historic black church in Charleston. The daughter of Indian immigrants was sharply critical of Trump during the election campaign.
Chief of Staff: Reince Priebus, 44
Head of the Republican National Committee, Priebus is a seasoned political operative who can build bridges between Trump and a skittish Republican leadership, particularly House Speaker Paul Ryan, a longtime ally.
Chief Strategist: Steve Bannon, 63
A key figure in Trump's victorious election campaign, Bannon served as the executive chairman of conservative news platform Breitbart, a favorite news source of the so-called "alt right," an offshoot conservative movement that embraces a mixture of populism, racism and white nationalism. His appointment, which does not require Senate confirmation, has been controversial.
White House Counsel: Donald McGahn
A former commissioner and chairman of the Federal Election Commission, McGahn represents "elected officials, candidates, national state parties, political consultants, and others on political law issues," as a partner at the Jones Day law firm in Washington.
Trump has led a contentious search for secretary of state. The prospective candidates touted most frequently have been erstwhile Trump critic and former Massachusetts governor Mitt Romney and outspoken former New York mayor Rudy Giuliani, along with disgraced general David Petraeus and Senator Bob Corker.
Those believed to be under consideration include Marine General John Kelly; Fran Townsend, the former Homeland Security advisor to president George W. Bush; and Congressman Michael McCaul, the head of the House Homeland Security Committee.