The aides aren't authorized to publicly discuss internal defense meetings and are speaking on condition of condition of anonymity.
When Pat Shanahan, America's acting defense secretary, started his new job on Wednesday, he made it clear to his staff what his chief focus would be: "China, China, China".
Trump also said that Shanahan, Mattis's deputy and a former Boeing executive, would serve as the acting defence secretary for "a long time".
But Trump, who has always been skeptical of open-ended military commitments in the Middle East, ultimately disregarded Mattis' counsel and opted for a drawdown of USA forces in Syria.
Appearing at Mr. Trump's side during Wednesday's Cabinet meeting at the White House on Wednesday, Mr. Shanahan said the Army Corps of Engineers was "dialed in" to help construct additional parts of Mr. Trump's Mexico border wall and that the Pentagon was exploring how to strengthen its support of the Department of Homeland Security's drive to curb illegal immigration.
Shanahan's focus on China will be in lock-step with President Trump and other members of the Trump administration, who have taken on China as the top economic threat to the country's future.
Under the direction of President Trump, the Department of Defense remains focused on safeguarding our nation.
A day earlier, at a White House meeting with congressional leaders, Trump called Mattis "our great military genius".
"I think the Chinese have been modernizing quite significantly in recent years, and that threatens our ability for freedom of movement. We're not talking about vast wealth", Trump said.
"It is very important that we support our allies and partners there and reassure them of our commitments", he said.
A Vietnam veteran, Webb briefly registered on the 2016 campaign's media radar when asked who he was most proud to have as an enemy, answering "I would have to say the enemy soldier that threw the grenade that wounded me, but he's not around right now to talk to".