With Michael Flynn out as national security adviser – the shortest tenure in the role in U.S. history – the search is on Tuesday to replace him.

CNN reports that Acting National Security Adviser Keith Kellogg is under consideration to fill the role permanently. Kellogg, a retired lieutenant general, "is a decorated veteran," a White House statement late Monday noted.

Kellogg is the National Security Council's chief of staff.

Acting National Security Adviser Keith Kellogg (U.S. Department of Defense)

Also under consideration, CNN reports, are retired Gen. David Petraeus and retired Vice Admiral Robert Harward. The New York Times reports that Harward is the leading candidate.

The Huffington Post reports that Stephen Hadley, who served as national security adviser to President George W. Bush from 2005 to 2009, is also under consideration for his old role.

Petraeus, the former CIA director, was considered by President Donald Trump to serve as secretary of state. The president opted instead for ExxonMobil CEO Rex Tillerson.

"I've been in a position before where a president has turned to me in the Oval Office in a difficult moment," Petraeus said in November. "The only response can be 'yes, Mr President.'"

Petraeus' appointment to any role remains widely controversial, however. He is still under criminal probation -- until April -- for divulging classified information as part of an extramarital affair. The scandal prompted him to resign as CIA director in 2012.