The news comes after Trump's firing of Secretary of State Rex Tillerson.
Trump did not make a formal offer to Perry when the two men met on Monday, the report said.
The Associated Press, citing a source familiar with White House discussions, reported Tuesday that Trump was considering replacing Shulkin with Energy Secretary Rick Perry in order to fix a plagued department whose morale has fallen even lower under Shulkin. CNN reported that the White House held private meetings with Shulkin, EPA Administrator Scott Pruitt, Interior Secretary Ryan Zinke and HUD Secretary Ben Carson last month to discuss the "optics" of their uses of taxpayer money. Although Perry's name has surfaced as a possible replacement for Shulkin, the president didn't ask Perry on Monday to take over Veterans Affairs, they said.More news: Fox News host calls Trump out for backpedaling on gun control
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Coffman initially called for Shulkin to resign in February after the report was made public. Embattled Secretary of Veterans Affairs David Shulkin is likely to be the next high ranking administration official to be fired.
Conservative veterans advocates fully supported Shulkin until a few weeks ago when the agency's inspector general said that he had improperly used government funds during a trip to Europe and his chief of staff tried to cover it up. Unlike Dr. Shulkin, who had run the department's health care system under President Barack Obama and spent a career in hospital administration, Mr. Perry has no background in health care delivery, but as Texas' governor, he showed a willingness to experiment.
Trump became irritated with Shulkin for publicly claiming that he has to fire people and purge his agency of Trump appointees, two people said. Russian Federation concedes "dozens" of civilians injured in Syria clash MORE to the White House last week and told him to stop creating drama in his agency, Axios reported Sunday. The two even attended Wimbledon after receiving tickets as a gift.