The Trump administration is pushing to conduct an on-site inspection of the Federal Reserve, as President Trump and his top aides continue to pressure Jerome H. Powell, the Fed chair, to lower interest rates or resign.

Russell T. Vought, the White House budget director, told reporters on Thursday that administration officials wanted to visit the Fed to observe the renovations at its Washington headquarters. The administration has asserted that Mr. Powell has mismanaged the project, resulting in a cost overrun, and it has demanded that he provide answers about the project to the Office of Management and Budget.

Mr. Trump has made clear that he is scrutinizing Mr. Powell because of the Fed’s approach to interest rates. The central bank has left borrowing costs unchanged for months as it looks to ensure that the president’s policies, particularly his steep and expanding global tariffs, do not cause inflation to worsen.

Hoping to pressure Mr. Powell into reducing rates, Mr. Trump has privately discussed firing him before his term expires in May 2026. On Tuesday night, Mr. Trump showed House Republicans a draft of a letter firing Mr. Powell and asked lawmakers if he should send it.

But the president may face significant legal obstacles if he proceeds. The Fed is independent of the White House, and a recent Supreme Court decision underscored the limited ability of the president to fire the Fed chair.

The primary grounds on which Mr. Trump could legally remove Mr. Powell would be if the chair engaged in some sort of egregious behavior, a standard that many experts say the White House has not met.