Retired general and former CIA Director David Petraeus has reportedly pulled his name from consideration to replace Michael Flynn as National Security Adviser.

According to a report by the Wall Street Journal Friday, Petraeus's name was floated for the role, but the White House was miffed by his concerns about staffing and independence. It's not clear how seriously he was being considered.

Still reportedly on the short list for the position are acting national security adviser Keith Kellogg, a retired three-star Army general and Flynn's chief of staff, former United Nations ambassador John Bolton, and Army strategist Lt. Gen. H.R. McMaster.

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The Washington Examiner reported that Kellogg, Bolton and McMaster will meet with Trump separately at his Mar-a-Lago resort in Florida this weekend to discuss the position, citing an administration official.

Former Army Chief of Staff and retired Gen. Ray Odierno is also believed to be under consideration, according to the Journal.

Texas Sen. Ted Cruz Rafael (Ted) Edward CruzLoeffler calls for hearing in wake of Netflix's 'Cuties' Health care in the crosshairs with new Trump Supreme Court list 'Parks and Rec' cast members hosting special reunion to raise money for Wisconsin Democrats MORE made a pitch for Bolton to get the position to CNN earlier Friday.

Flynn resigned from his post after reports that he misled White House officials about discussing sanctions on Russia with the country's ambassador to the U.S. before Trump took office.

Trump's top pick to fill the seat was retired Vice Adm. Robert Harward, who turned down the job, citing "financial and family issues."

However, contradictory reports have emerged over why Harward turned down the offer. According to a Financial Times report, a source familiar with Harward's decision said he was concerned about whether the top advisers in Trump's administration would allow him to install his own staff on the National Security Council. Flynn's deputy, K.T. McFarland, told The Hill on Tuesday that Trump had "asked that I stay on."

MSNBC's Chris Hayes reported Friday night that Harward's decision was not based primarily on staffing, but on the fact that the White House would not meet his conditions — and President Trump's press conference sealed the deal, a former national security official familiar with his decision told MSNBC.

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.

MSNBC reported that Harward sent a letter to the White House Thursday declining the offer. The White House then reportedly invited him to meet and asked him to reconsider, which he was open to. But after watching Trump's Thursday press conference, the source said, he made a final decision.

Petraeus said on Friday at a conference in Munich that anyone considering the job should have control over personnel and gain 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.

Officials told the WSJ that the White House wasn't open to Petraeus's demands.