Harward turned down the job after the White House resisted his demands to install his own staff on the security council, CBS News reported, citing two unnamed sources close to the situation.
At particular issue was the position of deputy national security adviser. According to CBS News' report, Trump told KT McFarland that she could keep her job after former National Security Adviser Michael Flynn resigned on Monday, but Harward refused to retain her as his deputy.
The Financial Times also reported that Harward turned down Trump's job offer, and cited two unnamed sources close to the situation.
One unnamed source familiar with Harward's decision said that he "was concerned" about whether Trump's top advisers would let him bring his own team onto the council, according to the report, and took particular umbrage at McFarland's retention.
He was "conflicted between the call of duty and the obvious dysfunctionality," an unnamed source with first hand knowledge of Trump and Harward's discussions said as quoted by the Financial Times.
Harward, a Navy Seal, served on President George W. Bush's National Security Council. He also served as Deputy Commander of the United States Central Command when it was under the command of General James Mattis, now Trump's secretary of defense.
Michael Flynn, Trump's former national security adviser, resigned late Monday days after reports revealed that he spoke about Obama-era sanctions in a call with Russia's ambassador to the United States before Trump's inauguration.
This contradicted members of Trump's administration, including Pence, who previously denied that Flynn and the ambassador discussed sanctions.