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.”

Next week’s hearing will begin a new phase in the inquiry, as the Judiciary Committee prepares to draft articles of impeachment related to charges that Mr. Trump abused his power to enlist Ukraine in tarnishing his political rivals. The committee is also expected to consider an article of impeachment charging that Mr. Trump obstructed the investigation by blocking witnesses from testifying and refusing to provide documents.

Democrats are also weighing whether to draft an obstruction-of-justice article based on the report by Robert S. Mueller III, the special counsel who investigated Russia’s interference in the 2016 election and the Trump campaign.

The bulk of the charges, however, will be based on evidence to be laid out in a detailed report by the House Intelligence Committee after weeks of public and private depositions of current and former administration officials on the Ukraine affair. The report, which Democrats have said will be submitted soon after Thanksgiving, is expected to charge the president with abusing his power by appealing to a foreign government for help in the 2020 presidential election. It will outline Mr. Trump’s efforts to pressure Ukrainian leaders to announce investigations of former Vice President Joseph R. Biden Jr. and other Democrats, while denying the country’s president a White House meeting and withholding nearly $400 million in military assistance.

“I remain committed to ensuring a fair and informative process,” Mr. Nadler wrote to Mr. Trump in his letter. He noted that he retained the right under the rules of the impeachment inquiry to deny the president participation in the proceedings if the White House continued to stonewall witnesses and other evidence.

Mr. Nadler gave the president and his lawyers until 6 p.m. Sunday to decide whether they want to be part of the Dec. 4 hearing.

The question of how much the president and his legal advisers decide to participate is likely to be a contentious one as his team wrangles with Democrats over Mr. Trump’s rights to present his defense to lawmakers and the public.

Lawyers for former Presidents Richard M. Nixon and Bill Clinton worked to some extent with the Judiciary Committee to present defenses for their clients during impeachment proceedings. But Mr. Trump and his allies on Capitol Hill have repeatedly criticized the Democratic-led impeachment inquiry as illegitimate.

In a letter to House Democratic leaders shortly after they formally opened the impeachment inquiry, Pat Cipollone, the White House counsel, said Mr. Trump would refuse to cooperate in any way with the inquiry.

“In order to fulfill his duties to the American people, the Constitution, the executive branch, and all future occupants of the office of the presidency, President Trump and his administration cannot participate in your partisan and unconstitutional inquiry under these circumstances,” Mr. Cipollone wrote.

On Tuesday, Mr. Trump claimed on Twitter that he “would actually like people to testify” as part of the inquiry because he believes they would say he did nothing wrong. But he also blasted the Democratic investigation, calling it a “phony Impeachment Hoax” and saying it is “a Democrat Scam that is going nowhere.”

A person familiar with deliberations among the president’s legal team said Wednesday morning that no decision had been made about whether to engage in a public defense of the president during the Judiciary Committee hearings.

Representative Doug Collins of Georgia, the top Republican on the Judiciary Committee, said in an interview on Wednesday that he would not blame the White House for declining to participate, underscoring skepticism among the president’s allies about whether it would be a fair forum for the president.