But a U.S. official told ABC News that neither the Army nor the Defense Department is investigating Vindman.
"That's going to be up to the military. We'll have to see, but if you look at what happened I mean, they're going to certainly I would imagine take a look at that," Trump had said on Tuesday.
"I think what he did was just reported a false call," said Trump in reference to how Vindman had characterized his July 25 phone call with Ukraine's president that had been at the center of the Trump impeachment.
“I have not seen that news,” Defense Secretary Mark Esper told reporters traveling with him to NATO meetings in Brussels Wednesday when asked about Trump's comments. "I’m not going to add anything more to what I already said I would just refer your questions at this point to the United States Army," he added.
“I’ve already spoken on this matter, like I said I refer these personnel matters to the United States Army, Esper said when pressed further.
But a U.S. official told ABC News that neither the Army nor the Defense Department was investigating Vindman.
Last Friday, after Vindman had been escorted out of the White House and asked if he would be welcomed back at the Pentagon -- and what the Pentagon would do to ensure he did not face retribution by the president or others -- Esper had replied, "We welcome back all of our service members wherever they serve to any assignment they're given."
"I would refer you to the Army for any more detail on that,' Esper added. "And as I said, we protect all of our persons, service members from retribution or anything like that. So we've already addressed that in policy and other means."
Shortly after President Trump's acquittal in the Senate, both Lt. Col. Vindman and his brother Yevgeny, also an Army Lt. Colonel, were both reassigned to the Army from their positions in the White House.
At the time an Army spokesperson confirmed that said that the Vindman brothers had been reassigned to the Department of the Army and that " out of respect for their privacy, we will not be providing any further information at this time."
National Security Adviser Robert O'Brien, in an interview at the Atlantic Council on Tuesday night, said that both brothers had been "reassigned" and that their being escorted out of the White House was "standard procedure."
O'Brien pushed back against the notion that both brothers were being retaliated against and that the U.S. is "not some banana republic."
"We are not a country where a group of lieutenant colonels can get together and dictate what the policy of the United States is," he said.
"The President is entitled to a staff that he has confidence in," O'Brien said. "I can absolutely tell you they were not retaliated against."