Names already circulating for Trump's next VA secretary nominee The Trump administration is back to considering new names to lead the VA.

With Adm. Ronny Jackson’s decision to remove his name from consideration as the next secretary of Veterans Affairs, the Trump administration has had to return to the drawing board to find a replacement, and interest groups and lawmakers are making suggestions.

At a news conference Friday, Trump said he had a range of candidates to choose from.

"I have many people who want the position, if you can believe it, with all this being said," he asserted, alluding to allegations against Jackson about unethical behavior on the job. Trump also called Jackson an "American hero."

While he suggested today that he had not yet narrowed down the list to one candidate, the president said Thursday that he already has someone in mind who has “political capability” – different from the career military physician Jackson.

But some veterans groups, like Iraq and Afghanistan Veterans of America, have already said that the top requirements on their wish lists are simple.

“Our veterans are simply looking for a competent, proven and dynamic leader with integrity that can lead our nation forward out of this storm of darkness and into a brighter future,” IAVA CEO and founder Paul Rieckhoff said in a statement.

Competence was also a quality emphasized by American Legion national commander Denise Rohan.

“We believe [the VA] is entirely manageable and effective when staffed with motivated, experienced and competent people. Our veterans deserve a properly led, efficient and transparent VA that delivers on the American people’s promises,” she said.

So who fits the bill?

At least one member of the Senate Veterans Affairs committee, who will be responsible for holding the confirmation hearing for the next nominee, suggested the acting secretary, Robert Wilkie, should take over. Sen. Bill Cassidy, R-La., said Wilkie “knows the situation” and could complete the confirmation process in relatively short order given his current position.

Trump himself praised Wilkie at an event Thursday with the Wounded Warrior Project, saying Wilkie is "doing a great job at the VA."

Cassidy, himself a physician, also suggested Delos “Toby” Cosgrove, who until recently was the president and CEO of the Cleveland Clinic.

House Speaker Paul Ryan commented on two members of his conference who he said would both make “fine” VA secretaries, Rep. Phil Roe, R-Tenn., chairman of the House Veterans’ Affairs Committee, and former congressman Jeff Miller, R-Fla.

He added that he had “no idea” who President Trump would ultimately pick, though both men would fit Trump’s description of someone having a political background.

The White House might also circle back to some of the candidates it was considering before Trump nominated Jackson, like Pete Hegseth, a former military officer and former CEO of the conservative Concerned Veterans of America.

If picked, Hegseth, a Fox News contributor, would fit with the president’s recent trend of pulling favorite TV pundits into the White House. In the past few months, Trump has replaced key advisers with contributors who have spent years outside of government, Larry Kudlow as the chairman of the National Economic Council and John Bolton as his new national security adviser – both of whom have spent years as cable pundits for CNBC and FOX respectively.

ABC's Katherine Faulders contributed to this report.