Some U.S. officials said Clarke will replace Army Gen. Tony Thomas, who is set to retire in 2019, once the Senate confirms him for the post.
Clarke was instrumental in the planning and execution of the 2011 raid that led to the death of Osama bin Laden during his time as an operations officer with Joint Special Operations Command in North Carolina.
The officials said the White House is expected to nominate Marine Corps Lt. Gen. Kenneth McKenzie, director of the Joint Staff, to succeed the retiring Army Gen. Joseph Votel as head of U.S. Central Command that is responsible for operations in the Middle East.
The Trump administration is also poised to nominate Air Force Gen. Tod Wolters as head of U.S. European Command and NATO supreme allied commander Europe.
Wolters currently leads Air Force Europe, Allied Air Command and Air Force Africa and is expected to replace the retiring Gen. Curtis Scaparrotti.
Navy Adm. Craig Faller has also been nominated by the White House to serve as head of U.S. Southern Command.