NEW YORK (Reuters) - U.S. President Donald Trump said on Wednesday he would prefer to keep Deputy Attorney General Rod Rosenstein in his job, after the New York Times reported Rosenstein had suggested secretly recording Trump and recruiting Cabinet members to remove the president from office.

“I’m talking with him. We’ve had a good talk. He said he never said it. He said he doesn’t believe. He said he has a lot of respect for me. And he was very nice. And we’ll see,” he said at a news conference, when asked if he would fire Rosenstein.

“My preference would be to keep him and to let him finish up,” Trump said, without explaining what he would like Rosenstein to finish working on.

Rosenstein currently oversees Special Counsel Robert Mueller’s independent investigation into possible Russian meddling in the 2016 presidential election. Russia denies interfering. Rosenstein is often the target of Trump’s anger.

Some news media reported on Monday that Rosenstein would soon leave his post, prompting Trump, in New York for the U.N. General Assembly, to say he would meet with the second-most powerful Justice Department official on Thursday. But Trump told the news conference he could delay the meeting for fear of distracting from a Senate hearing on Brett Kavanaugh, his embattled nominee to join the Supreme Court.

There had been widespread speculation that Trump would fire Rosenstein since Friday when a New York Times report said that in 2017 Rosenstein had suggested secretly recording the president and recruiting Cabinet members to invoke a constitutional amendment to remove him from office. The Times said none of those proposals came to fruition. Rosenstein denied the report as “inaccurate and factually incorrect.”

Shortly after the Times story, Trump told supporters at a rally in Missouri that there is “a lingering stench” at the Justice Department and that “we’re going to get rid of that, too.”

Rosenstein’s departure, though, could throw a cloud of confusion over the election investigation led by Special Counsel Robert Mueller, which Trump has called a “witch hunt,” and put its future in doubt.