In public testimony last week, Cohen told the House Oversight Committee that Trump's attorneys, including Jay Sekulow, had reviewed and edited the statement he provided to Congress.
Cohen subsequently pleaded guilty to lying to Congress in the testimony. Sekulow has called Cohen's assertion "completely false".
There are a host of topics that lawmakers are interested in hearing from Cohen about, including his public testimony about overhearing a conversation between Trump and longtime confidante Roger Stone involving a WikiLeaks' email dump, presidential pardons, and Cohen's public testimony that the Southern District of NY could be investigating his conversations with Trump.
Michael Cohen became a key figure in those investigations after turning on his former boss and cooperating with special counsel Robert Mueller's probe.
The issue is expected to come up again during Cohen's return visit.
Cohen's lawyer, Lanny Davis, said in a statement that Cohen has now spent 16 hours testifying before the intelligence committee. He also was interviewed privately by both the Senate and House intelligence committees last week and returned to the House intelligence panel behind closed doors on Wednesday.
There is nothing inherently improper about a subject in a criminal investigation seeking a pardon from a president given the president's wide latitude in granting them.
And the House Intelligence Committee has signaled interest in Weisselberg, while the panel's chairman Adam Schiff said the committee would hold a public hearing next week with Felix Sater, the Russian-born Trump business associate who worked with Cohen on the Trump Tower Moscow project.
"Cohen cooperated fully with the Committee... and provided important testimony and materials relevant to the core of our probe and that will allow us to advance our investigation substantially", Schiff said on Wednesday. "We also went through documents in our possession, dozens of documents in our possession with Mr. Cohen, but we have additional document requests that we will be in discussion with him about". Nadler said he would investigate possible obstruction of justice, corruption and abuse of power.
Federal prosecutors in NY have said Trump directed Cohen to arrange the payments to buy the silence of porn actress Stormy Daniels and former Playboy model Karen McDougal in the run-up to the 2016 campaign.
Cohen acknowledged in a guilty plea previous year that he misled lawmakers in 2017 by saying he had abandoned the project in January 2016, when in fact he pursued it for months afterwards as Trump campaigned for the presidency. Cohen told a judge that he agreed to cover up Trump's "dirty deeds" out of "blind loyalty".
"The fact that more independents are starting to question Trump's fitness for office could be a sign of trouble, if not for impeachment itself than for his re-election prospects in 2020", said Patrick Murray, director of the independent Monmouth University Polling Institute. He said the president arranged to reimburse Cohen, and Cohen took to the hearing a check that he said was proof of the transaction.