Harris, who was appointed by President Barack Obama, could end his term as head of Pacific Command (PACOM) after three years in May, two sources with knowledge of the potential change told Reuters. Most PACOM commanders serve three years but there is no official term limit.
A US official said that while the timing could be right, the process of replacing Harris - starting with a nomination to the Senate Armed Services Committee - had not yet begun.
"That definitely hasn't happened," the official said, speaking on condition of anonymity. "I would guess it maybe happens in the winter sometime."
"This is pure speculation, and no decisions have been made regarding the transition timing for the next commander," chief PACOM spokesman Captain Darryn James said.
"That said, the usual transition for combatant commanders is around the three-year point, and since Admiral Harris took command of PACOM in May 2015, his projected date has always been May 2018," Mr. James added.
Several US sources said Harris' departure would be part of normal rotation of command.
If Trump follows Obama's example, he will need to nominate a successor around September for approval by the US Senate by the year-end.
Those deliberations would come as Trump courts China to pressure North Korea to give up its nuclear and missile programs.
The appointment of his successor will be closely watched by Washington's allies in Asia.
The US sources said possible contenders to replace Harris included Admiral Scott Swift, also a strong proponent of freedom of navigation in the South China Sea and elsewhere, who has pushed for a bigger role for the US Navy Third Fleet in Asia.
Others were Admiral Philip Davidson, commander of the US US Fleet Forces Command, and Admiral Bill Moran, deputy chief of naval operations.
Should the traditional navy post go to another service, General Terrence O'Shaughnessy, commander of Pacific Air Forces, could be in line, analysts say.
Harris has had to shore up US alliances in Asia amid concerns that Trump's decision to quit the Trans-Pacific Partnership trade pact and the Paris climate accord could signal a US withdrawal from a global role.
"American leadership matters greatly to our allies, partners and even our adversaries in the Indo-Asia-Pacific," Harris said in an emailed statement to Reuters this month.