WASHINGTON — The White House is reviewing an invitation from House Democrats for President Trump’s legal team to participate in the first Judiciary Committee impeachment hearing next week, even as his lawyers privately question whether to engage with a proceeding his administration branded “an illegitimate sham partisan process” to drive Mr. Trump from office.

Representative Jerrold Nadler, Democrat of New York and the chairman of the Judiciary Committee, wrote to the president on Tuesday offering him or his lawyers the opportunity to appear before lawmakers at a Dec. 4 hearing with constitutional scholars to discuss the historical precedents for impeachment, the definition of an impeachable offense and whether Mr. Trump’s actions meet the bar for removal.

In a statement on Wednesday, Stephanie Grisham, the White House press secretary, did not give any indication about whether Mr. Trump or his lawyers intended to accept the invitation. But people familiar with the president’s legal strategy have said privately that they are deeply suspicious of taking part in a process they view as unfair to Mr. Trump.

“What is obvious to every American is that this letter comes at the end of an illegitimate sham partisan process,” Ms. Grisham said in the statement. “The president has done nothing wrong, and the Democrats know it.”