WASHINGTON — White House officials said on Thursday that President Trump and Deputy Attorney General Rod J. Rosenstein will meet next week to discuss Mr. Rosenstein’s future at the Justice Department.

The New York Times reported on Friday that Mr. Rosenstein had suggested secretly recording Mr. Trump to document the chaos of the White House in 2017 and had raised the issue of removing the president from office.

That prompted Mr. Rosenstein to tell senior White House advisers over the weekend that he was willing to resign. On Wednesday, Mr. Trump said that was not his preferred outcome and that Mr. Rosenstein had denied the reports.

“I’m talking to him. We’ve had a good talk,” Mr. Trump said. “He said he never said it. He said he doesn’t believe it. He said he has a lot of respect for me, and he was very nice, and we’ll see.”