Mr. Stewart, like other Republicans on the House Intelligence Committee, vigorously defended Mr. Trump during impeachment hearings in the fall that focused on the president’s pressure campaign on Ukraine. And he has been sharply critical of the handling by the Justice Department and F.B.I. of an investigation into the Trump campaign’s ties to Russian interference in the 2016 election.

“They want to take away my vote and throw it in the trash,” Mr. Stewart said of Democrats just before the impeachment vote in the House. “They want to take away my president and delegitimize him so he cannot be re-elected.”

Mr. Stewart, 59, has long been interested in the post of intelligence chief, people close to him said. He is well-liked by congressional Republicans and is thought to enjoy support from Senate Republicans, who would confirm him if he is nominated.

But Democrats are likely to balk at the selection of a House lawmaker with such a political track record. Senate Republicans could have the votes to approve on their own a nominee like Mr. Stewart, but some have said they want to see a nominee with bipartisan support. Senator Richard Burr, Republican of North Carolina, who leads the Senate Intelligence Committee, was cool to Mr. Ratcliffe’s nomination and is likely to influence the White House’s ultimate choice.

The clock is ticking on a decision. Mr. Maguire cannot serve past March 11 under federal law. Before then, the administration must have a director nominated and confirmed or be forced to find a new acting director.