The new legal team that former President Donald J. Trump has brought in for his impeachment trial next week is unlikely to focus his defense on his baseless claims of widespread election fraud and instead question whether the trial is even constitutional since he is no longer president, people close to the team said on Monday.

Several Trump advisers have told the former president that using his election claims as a defense for his role in the mob attack on the Capitol last month is unwise, according to a person close to the new lawyers, David Schoen and Bruce L. Castor Jr. The person said the former president’s advisers did not expect that it would be part of the arguments they make before the Senate.

In an interview with The Atlanta Journal-Constitution on Monday, Mr. Schoen confirmed that he would not make that argument. “I’m not in this case for that,” he said.

Mr. Schoen, an Atlanta-based criminal defense lawyer, and Mr. Castor, a former district attorney in Pennsylvania, replaced Butch Bowers and four other lawyers working with him after they parted ways with the former president.

A person close to Mr. Trump said there was disagreement about the approach to strategy, as he pushed to have the legal team focus on election fraud. The person also said that the former president had no “chemistry” with Mr. Bowers, a South Carolina lawyer recommended to him by Senator Lindsey Graham, one of his most loyal supporters.

A second person close to Mr. Trump said that Mr. Bowers had seemed “overwhelmed” by the case and confirmed a report from Axios that the lawyer had sought about $3 million for fees, researchers and other expenses.

The new team has to file a brief with the Senate on Tuesday that will provide a first glimpse of how they plan to defend the former president. Mr. Trump never had an opportunity to offer a defense in the House impeachment proceedings because of the speed with which they were conducted.

Senator John Cornyn, Republican of Texas, warned Mr. Trump’s team on Monday to stay away from rehashing his inflated grievances and debunked theories about election fraud. Better, he said, to focus on rebutting the particulars of the House’s “incitement of insurrection” charge.

“It’s really not material,” Mr. Cornyn told reporters in the Capitol of Mr. Trump’s repeated claims. “As much as there might be a temptation to bring in other matters, I think it would be a disservice to the president’s own defense to get bogged down in things that really aren’t before the Senate.”

Many Republicans on Capitol Hill expect the defense team to at least partly rely on their argument that holding a trial of a former president is unconstitutional. People close to the Trump legal team said that would be a main avenue of defense, and Mr. Schoen told The Journal-Constitution that the constitutional question would be key.

Mr. Schoen also said he planned to argue that Mr. Trump’s language did not “constitute incitement” of the violence on Jan. 6, when a mob of Trump supporters stormed the Capitol. But not all of the former president’s advisers share the belief that such an argument should be made; some have said privately that it is unnecessary to debate the key focus of the impeachment articles.

The constitutional debate around that issue — many scholars disagree, citing the fact that the Senate has tried a former official in the past — will figure significantly in the trial. In preparation, the Senate has explicitly asked both sides to address in their written briefs “whether Donald John Trump is subject to the jurisdiction of a court of impeachment for acts committed as president of the United States, notwithstanding the expiration of his term in said office.”

The House managers are set to file their own, more detailed legal brief on Tuesday. The document should offer the first comprehensive road map of their argument that Mr. Trump sowed baseless claims of election fraud, summoned his supporters to Washington and then directly provoked them to confront Congress as it met in the Capitol to certify his election loss.

The brief will also include an argument in favor of holding the trial, with the managers prepared to argue that the framers of the Constitution intended impeachment to apply to officials who had committed offenses while in office.

A similar document from Mr. Trump’s team to expand on their initial pleading is due next week before the trial begins on Feb. 9.

Some around the former president have suggested arguing against the central accusation in the impeachment article — that he incited an insurrection — and instead focusing more closely on process issues like the constitutionality of the case.

While the lawyers were just named, Mr. Schoen has been speaking to Mr. Trump and others around him in an informal capacity for several days, people close to the former president said. Mr. Schoen has represented a range of clients, like mobsters and Mr. Trump’s longtime adviser Roger J. Stone Jr.

Mr. Castor is best known for reaching a deal not to prosecute Bill Cosby for sexual assault when he was the district attorney of Montgomery County, Pa. He also briefly served as the state’s acting attorney general.

Mr. Castor’s cousin is Stephen R. Castor, the congressional investigator who battled Democrats over Mr. Trump’s attempts to pressure Ukraine to investigate Joseph R. Biden Jr. when he was preparing to run against him. A person familiar with the discussions said that Stephen Castor had recommended his cousin to the former president.

It is unclear how close the Castor cousins are. Stephen Castor is a veteran of some of Capitol Hill’s most fiercely partisan oversight disputes in the past decade. He worked on investigations into the Obama administration’s handling of an attack on the American diplomatic mission in Benghazi, Libya, and a gun trafficking program known as Operation Fast and Furious.

In the meantime, the nine House impeachment managers have all but gone underground in recent days, favoring private trial preparations to the kind of TV interviews and other public appearances often used in Washington to try to shift public opinion.

Democratic leaders are trying to carry out both the president’s lengthy legislative agenda and a major impeachment trial of his predecessor more or less simultaneously. The decision to maintain a low profile was apparently driven by the desire to divert as little attention as possible from Mr. Biden’s push for coronavirus relief legislation, the priority issue of his agenda.