Washington(CNN) President Donald Trump's attorneys are trying to sway him against agreeing to an interview with special counsel Robert Mueller partially out of concern he might incriminate himself through false statements and could be charged with lying to investigators, The New York Times reported Monday evening.

The report follows on CNN's reporting last week that Trump's attorneys are arguing that Mueller's team has not met the "high threshold" it needs to have Trump in a face-to-face interview.

The Times, citing four people briefed with the matter, said Trump's attorneys want the President to refuse an extensive interview with Mueller's team and that lawyers and aides believe once refused, Mueller may not be willing to subpoena Trump in an attempt to compel a presidential interview.

Trump said last month that he wanted to speak with Mueller and would be willing to do so under oath.

"I am looking forward to it, actually," Trump told reporters. "Here is the story: There has been no collusion whatsoever. There is no obstruction whatsoever. And I am looking forward to it."

After Trump made that remark, his attorney John Dowd said he would be the one to decide whether Trump talks to the special counsel and that he had not made a decision yet. The Times report on Monday said Dowd "wants to rebuff an interview request."

As the Mueller-led special counsel investigation into potential coordination between Trump associates and Russia to influence the 2016 election, and questions about any possible obstruction of justice, continues, more attention has fallen onto the prospect of a potential sit-down interview with Trump.

Sources familiar with the matter told CNN late last month that Mueller had provided Trump's lawyers with a range of topics he wants to ask Trump about in the interview.