US President Donald Trump speaks during a campaign rally at the Florida State Fairgrounds Expo Hall in Tampa, Florida, on July 31, 2018.

President Donald Trump has prodded his attorneys in recent days to arrange for him to be interviewed by special counsel Robert Mueller's team, despite their warnings that doing so could increase his legal exposure, The New York Times reported, citing three people briefed on the matter.

Trump believes, in effect, that he can convince prosecutors that the inquiry is a "witch hunt," and bring the investigation to a quick conclusion, the Times reported. On Wednesday, the president demanded that Attorney General Jeff Sessions end the probe "right now," though the White House later said the directive was an "opinion," not an order.

The special counsel's office declined to comment. The White House referred questions to the president's outside counsel.

Read more: Trump is tweeting the term "witch hunt" more frequently these days

The president's outside attorney, former New York Mayor Rudy Giuliani, told reporters Wednesday that the special counsel's team had submitted its latest a proposal for an interview on Tuesday. Negotiations about the contours of a potential interview have stretched on for months.

"They sent us a proposal. We responded to their proposal. They took about 10 days, and yesterday we got a letter back from them, and now we're in the process of responding to their proposal," Giuliani said.

Giuliani said he didn't want to give reporters "hope" that the interview would happen, but said the president "has always been interested in testifying." He said that he, and the other attorneys representing the president, "have the most reservations."

"I don't know if you find a lawyer on television that ever thinks their client should testify," Giuliani said.

Trump has publicly said he wants to sit down for an interview with the special counsel. In a January press conference, the president said he was "looking forward to it."

In their proposal Tuesday, Mueller's investigators said they wanted to discuss links between Trump associates and the Russian government, and whether Trump has obstructed justice, the Times reported.