Days before the Federal Reserve is set to vote on whether to lower interest rates, the central bank isn’t even sure who will attend the pivotal meeting.

The ability of Lisa Cook, a Fed governor, to vote next week was thrown into doubt on Thursday after the Trump administration asked a federal appeals court to allow the president to remove her from her post while a lawsuit she has filed contesting her firing proceeds.

At the same time, Stephen Miran, President Trump’s pick for a separate Fed seat, could be confirmed by the Senate as early as Monday night, allowing him to cast a vote at next week’s meeting, which kicks off on Tuesday.

The last-minute uncertainty over who will cast a vote stems from Mr. Trump’s desire to exert more influence over the Fed’s interest rate deliberations. The president has spent months castigating the Fed for not lowering borrowing costs and has begun trying to reshape the central bank with loyalists who share his belief that rates should be much lower.

Interest rate decisions are made by the seven-person Fed board as well as a rotating group of five regional presidents from the Reserve Banks around the country.

Removing Ms. Cook and putting Mr. Miran in place by Wednesday’s vote will not materially alter the Fed’s final decision — the central bank is poised to begin lowering interest rates after an extended pause. But it underscores the tumult that likely lays ahead as Mr. Trump continues his onslaught on the institution.