Washington (CNN) Close advisers and friends of President Donald Trump are warning him not to sit for an interview with special counsel Robert Mueller, with some expressing skepticism that there would be any circumstance in which it makes sense to voluntarily submit to an interview, according to multiple sources familiar with the ongoing discussions.

The President has told friends he's willing to talk with Mueller -- the man Trump views as leading a "witch hunt" against him -- to make the case there was no wrongdoing, sources told CNN. White House special counsel Ty Cobb says the White House is cooperating with Mueller's investigation into potential collusion between the Trump team and the Russians in the 2016 election.

Some key allies on Capitol Hill also are urging Trump to avoid potential political and legal jeopardy and not answer questions from Mueller. They are part of a group of supporters ranging from lawyers on the Trump team and in the White House orbit to friends who say it would be unwise for the President to talk. Others say Trump should find a way to cooperate that limits his potential legal exposure.

Mueller hasn't yet requested a Trump interview but has indicated he wants to talk with the President. In the end, much depends on the course Mueller takes and whether the two sides can reach a deal or end up having a lengthy legal fight to decide the issue.

Trump's legal team is weighing "every possible avenue" for the President to provide information to the special counsel, from interviews to written answers. One source said the result "could end up being some sort of hybrid" and that the whole thing is "under deep discussion."

Gaming out the legal strategy

The lawyers' decision will be influenced by what topics Mueller wants to question Trump about and whether the information can be obtained elsewhere, sources familiar with their thinking say.

Among the possible scenarios: whether the interview is merely a box to check to finish an investigation, as with Hillary Clinton's interview about the private email server; whether Mueller wants the President to speak as a witness to others; or whether it becomes a full examination of a target of the investigation.

The President and his lawyers are hoping Mueller will wrap up the investigation soon. One way to do that, some believe, would be to have the President respond to questions in some form. If Trump's lawyers do agree to an interview, the President's legal team also will need time to prep him as a witness.

On Wednesday, Trump provided some public insight into his own thinking.

A source from the President's legal team said Trump "got a little ahead of himself" in his comments about the meeting with Mueller's team. "We haven't closed any doors," the source said. "We haven't made any decisions."

White House press secretary Sarah Sanders said Thursday the President's position has not changed.

"We're going to continue to be fully cooperative with the special counsel as we have been. However, the president and his personal attorneys are going to discuss this matter with the office of the special counsel, not reporters, and that's going be the process that we follow," Sanders said.

Still, friends and allies caution Trump should think twice about talking.

A source who is close to and speaks with the President has advised him against talking to Mueller's team. The source says that even though the President did nothing wrong, he will put himself in jeopardy if questioned in a recorded interview.

The source is concerned that no one around Trump is telling him the truth about the realities of this investigation, which has spread beyond inquiries into collusion with Russia to questions about whether the firing of Comey was obstruction of justice.

A friend of Trump's said the question of whether he should directly speak with Mueller's team is a "continual debate. He wants to testify. This is obviously a gigantic tactical issue."

The President, he says, is too eager. "He says 'Just let me at it', and that's the problem."

Another longtime adviser says he shouldn't have to do an interview under any circumstance as a matter of policy and principle

The conventional wisdom among lawyers is to not put a client in front of prosecutors without any kind of immunity or assurances about potential legal jeopardy.

Steven Schlesinger, an attorney who worked for Trump on several lawsuits he fought with Deutsche Bank and other banks over loans, said he doesn't expect Trump will speak with Mueller's team.

"In my humble opinion, the shot of him actually testifying is near zero," Schlesinger said Tuesday.

Hill reservations about risks of an interview

Trump's Capitol Hill allies are also concerned, with some telling CNN he should proceed cautiously -- and seriously consider avoiding any talks with the special counsel.

Their fear: Trump could imperil his presidency with a mistake before Mueller's team, and it's simply not worth the risk.

"If I was the President's lawyer, I would not advise doing that," said Rep. Matt Gaetz, a Florida Republican, lawyer and sharp Mueller critic. Gaetz added, "I think the entire Mueller probe is infected by intractable bias. And the President only risks some inadvertent misstatement becoming a new national narrative by doing that."

Rep. Steve King, a conservative member of the House Judiciary Committee, urged Trump to only agree to answer written questions.

"This is pretty much unprecedented .... there is not any evidence of anything," the Iowa Republican said. "The better path is to answer these in writing -- and see what those answers are and hopefully they're complete and true."

Texas Sen. John Cornyn, the No. 2 Senate Republican who serves on the Senate Judiciary and Intelligence Committees, said it would make sense for the President to be "cooperative."

Republican Sen. Thom Tillis, a member of the Senate Judiciary Committee, said he had no issues with Trump talking to Mueller's team. But he said the lawyers need to set limits regarding what would be covered in the interview.

"It's good due diligence by his legal team on the part of his legal counsel to clearly know what the parameters are," Tillis said.

Tillis said the lawyers should make clear to Mueller's team that they "want to stay focused on the matter of the investigation."