White House press secretary Sarah Huckabee Sanders says the president is "committed to the rule of law and will work with members of both parties to reach a permanent solution that corrects the unconstitutional actions taken by the last administration".
After Bannon left the White House in August, he remained on good terms with Trump.
US President Donald Trump walks to Marine One before leaving the White House on January 5, 2018.
Burck, who is a former special counsel and deputy counsel to George W Bush, is also representing Bannon exclusively in the House of Representatives intelligence committee interview relating to his time as campaign chairman for Trump.
Boyle is a long-time Bannon protege who has shaped Breitbart's political coverage.
President Donald Trump Trump responded at the time by slamming Bannon in a fiery statement, saying Bannon had "lost his mind".
Steve Bannon to Step Down From Breitbart News
Mr. Bannon had already been on the outs with his former Prince for taking all the credit for the latter's improbable and regrettable election victory. "Moreover, the book appears to cite to no sources for many of its most damaging statements about Mr. Trump".
The White House had filed a cease-and-desist order to block the book's release, but publisher ignored the challenge and published the book ahead of its scheduled release date. Mr. Bannon and Mr. Kushner had famously bonded during the campaign. He returned to his earlier job and original passion - as head of Breitbart, warring against the Republican establishment. This is the first time a Democrat has won a senate seat in the deeply conservative state of Alabama in 25 years. But he has a skill set that makes him a valuable partner in American right-wing politics, and hence his political obituary should not be written in a hurry. A person familiar with the matter confirmed the representation but said Burck was advising Bannon only in relation to the House committee interview and his time on the presidential campaign.
On Tuesday, Trump met with a bipartisan team in the nation's capital to discuss comprehensive immigration reform and amnesty for undocumented immigrants, of which Bannon was an outspoken critic.
"I know that when I write e-mails seeking interviews, my word choice is to say, I will treat the individual with dignity and respect".