Given a chance to comment on her relationship with President Donald Trump, Fed Chair Janet Yellen demurred. However, she said rapport elsewhere within the administration is solid.

The central bank chief was asked during a discussion in London about how things are going between her and a president who once said she should be "ashamed" of the way she's led monetary policy.

"I'm not going to comment on my relationship with the president," she said. "I will say that it's been a very long tradition in the United States for Federal Reserve officials to have good and close working relations with our counterparts in the administration. There's a long history, I don't know, going back decades of regular meetings of Treasury secretaries and Federal Reserve chairs."

In the current administration, that would mean Treasury Secretary Steven Mnuchin.

"I've continued that tradition with Secretary Mnuchin, and we confer about the economy and the outlook and issues pertaining to financial regulation, and we both have interests and responsibilities," she said.

There has been much speculation about whether Trump will retain Yellen as Fed chair when her term runs out early next year. Yellen also has evaded making guesses about that scenario as well, though tradition would indicate that she'll find out sometime in August.

For now, she's focusing on keeping the discussion going with Mnuchin.

"I would say that I've got a good working relationship [with Mnuchin]," she said. "I've found solid respect for the independence of the Fed."