"No," Powell responded when asked by the moderator at the American Economic Association's annual meeting: "If the president asked you to resign, would you do it?"
Powell also said he had not received any direct communication from the White House about unhappiness with the central bank's rate policy, and no meeting with Trump has been scheduled.
"I would say that meetings between presidents and Fed chairs do happen," was all that Powell said when asked if he would meet with the president.
Trump appointed Powell but has become severely critical of the Fed chairman. In October, Trump said the Fed was "going loco" as it continued to tighten monetary policy. The Fed raised rates four times in 2018. In December, a report said Trump wanted to fire Powell as his frustration with Fed policy and the market's downturn increased.
The Dow Jones Industrial Average and S&P 500 last month posted their worst December performance since 1931, falling more than 9 percent each. The S&P 500 also notched its biggest annual loss since the financial crisis, dropping more than 6 percent.
When asked if Trump's approach to the Fed is problematic, former Fed chairman Ben Bernanke — who was on the same panel as Powell — said: "Yeah I think everyone would be better off if it was clear that the Fed is making its decision based on its mandate and on its assessment of long-term needs in the economy which I'm completely confident that it will do."
It's not exactly clear whether the president can fire the Fed chairman. The Federal Reserve act does state a governor of the central bank can be removed for cause by the president but "cause" is not defined. Analysts say it isn't likely disagreement over monetary policy applies.
—CNBC's Yun Li and John Melloy contributed to this report.