President Trump's top personal lawyer said Tuesday that his legal team is still deciding whether to "accept the proposition" of responding to the special counsel's request for written answers regarding the Russia investigation.

Jay Sekulow’s comments came after a New York Times report—citing two people briefed on the matter-- said that Special Counsel Robert Mueller would accept written answers on questions about whether the president's campaign conspired with Russia's election interference.

“But I will tell you this, I’m not concerned about the President of the United States responding, if we decide to accept the proposition of responding to written questions, responding to questions about Russia and interference with the election,” Sekulow told Fox News’ ‘Hannity.’

Sekulow said Trump’s lawyers and Mueller’s team have “an ongoing dialogue." He said that he’s not going to “discuss the contents of what has been agreed to or not agreed to.”

Sources told Fox News, though, that Mueller’s team has come “closer” to the conditions Trump’s attorneys have been seeking and they will respond to the latest letter.

Mueller did not say he would be giving up on an interview altogether, including on questions of obstruction of justice, according to The Times. Mueller also reportedly did not ask for written responses on the obstruction investigation.

Sekulow did not address the obstruction investigation, but primarily discussed the Russia investigation portion, saying “I’m not worried about questions on Russia.”

“The President is committed. There’s no crime here, no underlying crime that the president was involved in. I’m not concerned about where that goes. Look, if they ask questions, and we think they’re appropriate, we would respond,” Sekulow said.

He pointed out that Trump’s legal team has handed over 1.4 million pages of documents to the special counsel’s office.

“This White House has been the most transparent in history when it comes to investigations or inquiries like this,” Sekulow said. “This needs to come to an end.”

He said he doesn't give specific times or dates as to when he thinks the investigation should end, but that “it needs to happen sooner than later.”

“Because at the end of the day as I said, it’s a process of negotiation,” Sekulow said.

Fox News' John Roberts contributed to this report.