The US president’s frequent “inability to find words” could be the result of “small strokes,” David Scheiner suggested.
His comments came during a CNN interview about Mr Trump’s unexpected weekend hospital visit, which has prompted speculation about his health.
“If he had an MRI of his head over there, I would be very pleased because I think he needs it,” said Mr Scheiner of the president’s two-hour trip to Walter Reed National Military Medical Centre on Saturday.
Addressing Mr Trump’s often rambling and occasionally incoherent speech, the doctor said: “These aren’t slips of the tongue, these are words he can’t find and this is happening over and over again.
“Comedians joke about it, but it’s not a joking matter. I think there is a neurological issue that is not being addressed.”
Mr Scheiner, who was Mr Obama’s doctor for 19 years before he was elected president, added: “The worry that I have is maybe he’s having small strokes. We’ve had that once before in the White House when Woodrow Wilson was president.
“His inability to find words is peculiar and has not been explained, and I think one has to think of it as a possible neurological issue.”
The White House has insisted the president’s hospital visit – which, unusually, was not mentioned on his weekly schedule - was was for “routine” tests as part of his yearly medical check-up.
His doctor Sean Conley said in a statement issued on Tuesday: “Despite some of the speculation, the president has not had any chest pain, nor was he evaluated or treated for any urgent or acute issues. Specifically, he did not undergo any specialised cardiac or neurologic evaluations.”
But the official explanation has been met with scepticism as Mr Trump underwent his last annual physical only nine months ago and is known to have dictated statements issued by his doctors boasting of his “astonishingly excellent” health.
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