Cohen is not expected to answer questions on any issues pertaining to that investigation when he appears before the House's Monitoring Committee next month because Specialist Robert Müller's investigation is underway. He consulted with the Special Adviser before arriving to hear during the hearing, two sources told CNN.
That doesn't mean that Coh's testimony won't get dramatic revelations.
Cohen is prepared to discuss issues relating to housekeeping payments and aspects of the Trump organization, including the roles of the President and his children, according to a source familiar with the matter.
Cohen is willing to detail – if asked – then candidate Trump's role in directing payments to two women who have claimed they had business with Trump and how his election played a role in it, according to the source. Trump has denied business with the women. Cohen may also talk about how he believes his prison for tax evasion is unfair, the source said.
Cohn's testimony has raised questions about what he can publicly say that the Mueller probe continues.
House Chairman Elijah Cummings said his staff consulted with Mueller about Coh's appearance and will continue to do so before his February 7 hearing.
"We will not interfere with the Mueller investigation," said Maryland Democrat Friday. "These discussions (with special advice) may well progress to the day before … because Mueller is running."
Cohen appears before Congress next month after he alleged guilty in December for several accusations and sentenced to three years in prison. Cohen pleaded guilty to campaign finance crimes that included payments during the campaign to silence women's alleged affairs – crime prosecutors say Trump directed Cohen to commit. Trump has denied that he ruled Cohen to make the payments.
Cohen also pleaded guilty to lying to Congress about how long the proposed Trump Tower Moscow project discussions were extended to the 2016 campaign when he testified before the Congress Intelligence Committee 2017.  It is not yet clear which specific topics may be limited. Cummings refused to say, for example, if Cohen would be allowed to talk about Trump Tower Moscow.
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" The American People will have the opportunity to hear from him, Mr Cohen, "Cummings said. "And their representatives, who are representatives on the Republican side and the Democratic side, will have the opportunity to ask questions to him, and I believe that the American people would see that it played a role, their voices played a role and we opened it for transparency. "
A democratic member of the panel warned the Democrat Democrats not to give Republicans what they want – turn their hearing into a circus by asking intimate questions about Trump's alleged affairs.
Coh's testimony before the surveillance panel is public, so he won't talk about Russia's investigation there, but he could get these discussions with Congress behind closed doors before other panels. Both the Parliament's and Senate's intelligence panels are trying to recover Cohen before he reports to jail in March.
"I understand that he does not intend to deal with Russia's investigation into his open testimony. He will have to answer questions about it and we are in contact with the lawyer," said House Intelligence President Adam Schiff in California to CNN on Thursday "We hope he will voluntarily testify before the Intel Committee at the end of the session."
According to a source familiar with the matter, Cohen has not yet undertaken to testify to any of the intelligence committees.
Although Mueller does not want Cohen to answer questions related to Russia's investigation, it does not mean that they will not be asked at their public hearing. Ohio Rep. Jim Jordan, the Supreme Republican in the Supervisory Committee, does not rule out pressing Cohen on issues related to anything topic
"It seems to me if he comes in there should we be able to ask him what we want to ask him about," Jordan said on Friday.
On Friday, Jordan sent a letter to Cummings and asked him to include Republican co-workers in discussions with Cohn's lawyers and Mueller's team on Coh's testimony. Jordan also asked Cummings to apply for a number of records from the Justice Department and the FBI on Cohen, including notes of their interviews with Cohen, investigation reports and cooperation agreements.
"I hope you will work with me and the minority members to avoid an unproductive and chaotic hearing," Jordan wrote. "If you are to provide a platform for the convicted felon and perjours, we should make sure we have the necessary information to prepare ourselves to question him."
Jordan was often frustrated when Republicans investigated the FBI and the Justice Department in 2016 that his questions about the origin of Russia's investigation and a foreign intelligence monitoring order were rejected by DOJ lawyers.
"I have tried to ask all kinds of questions in all these deposits and I have had 15 lawyers sitting in there and tell the witness that they could not answer the question," he said.
"For one and a half year (the Democrats) we said that we do not want to do anything to interfere with the Mueller investigation, but we "will take in their star witness before the Mueller investigation is completed."
Rep. Mark Meadows of North Carolina, the House Freedom Caucus chairman and a close GOP ally with Trump on the surveillance panel, suggested what Akrimony Cohen should expect from the Republican issues.
"I find it strange that the very first big hearing, the witness is a convicted felon who comes to jail for lying to the congress, Meadows said.
Cohen could use his will to testify as a way to appeal a more impaired sentence, but there is no contract with prosecutors to consider it, he is due to start his three-year sentence on March 6.