Retired Gen. David Petraeus has reportedly taken his name out of consideration for the job of national security adviser after it was reported Thursday that Retired Vice Adm. Bob Harward, Trump's original pick to fill the NSA position left vacant by the departure of Michael Flynn, had turned down the offer.

According to The Hill, Petraeus, speaking from a conference in Munich on Friday, said a condition of accepting the job should be control over personnel, as well as a commitment from the White House to have a "disciplined process for crafting security policy."

“Whoever it is that would agree to take that position certainly should do so with some very, very significant assurances that he or she would have authorities over the personnel of the organization, that there would be a commitment to a disciplined process and procedures,” Petraeus said at the Munich Security Conference.

The Hill reports that the White House would offer Petraeus no such assurances.

Harward, a confidante of Secretary of Defense James Mattis and a widely admired individual in the national security world, was said to have similar concerns when he turned down the job Thursday.

MSNBC's Chris Hayes reported Friday that Harward's decision differed from Petraeus' in the area of staffing, but that he shared the general's concern that the White House would not meet his conditions.

From The Hill:

Harward had reportedly wanted a clear chain of command and direct line to Trump in which he was the sole national security adviser. He also wanted the structure of the National Security Council to be restored to the model of past administrations so that political advisers, namely Steve Bannon, would not have a seat at the key Principals Committee.

Harward was asked by the Trump administration to reconsider his decision, and was open to discussion, but made a final decision to turn the offer down following Trump's Thursday press conference, notes The Hill.

The president is reportedly now considering acting national security adviser Keith Kellogg, a retired three-star Army general who served as Mr. Flynn’s chief of staff, for the job. Kellogg traveled with Trump to South Carolina Friday for a speech there.

“General Keith Kellogg, who I have known for a long time, is very much in play for NSA—as are three others,” Trump said on Twitter Friday morning.

The Wall Street Journal reports that people familiar with the process say the list of names who might be considered include former United Nations Ambassador John Bolton, Army strategist Lt. Gen. H.R. McMaster and former Army Chief of Staff and retired Gen. Ray Odierno.

The Blaze reported Thursday that Flynn's resignation came after Trump lost trust in him over misleading Vice President Mike Pence over communication he had with a Russian official before the election. The affair has led for calls for an investigation over possibly illegal interactions between Trump's campaign aides and Russia.