"We would be inclined to do it", Giuliani said of a potential interview, which could touch on Trump's firing of Federal Bureau of Investigation director James Comey.
"The President wants to get this behind him, so he can keep the country safe", Cobb said referring to the investigation.
Earlier this month it was reported the president has hired a husband-and-wife legal team, Jane and Martin Raskin, who run a law practice in a suburb of Miami, Florida.
Flood, 61, brings to the White House an impeccable resume in the conservative legal community and a top-notch reputation among Republican and Democratic colleagues.
Flood also clerked for Supreme Court Justice Antonin Scalia.
It is, of course, in the best interests of any mysterious unnamed White House source to portray their boss as the kind of guy who's ready to knuckle up whenever he's backed against a wall. Now, the White House is anticipating a possible legal showdown over a presidential interview.
Incidentally, a study published Wednesday by the American Sociological Review found that Trump supporters justified Trump's lies as a form of "symbolic protest."
Still, his retirement is the latest evolution for a legal team marked by turnover.
He had reportedly urged the president to allow himself to be interviewed by Mr Mueller in order to hurry along the inquiry that is overhanging his presidency.
"Some people have talked about a possible 12-hour interview", Giuliani told the Post.
Adding Mukasey to the President's roster of lawyers outside the White House is under consideration, but sources cautioned that a final decision has not been made.
Joshua Stueve, a spokesman for Mueller, declined to comment on the reports. Trump attorney Jay Sekulow declined comment as well. But Dowd resigned in March, prompting a total overhaul of Trump's team that has now led to Flood's hiring.
Both Trump and Moscow deny any wrongdoing, and the president has called the investigation a political witch hunt.
"There is a time to sow and a time to harvest". His view of Mueller soured further after raids last month that targeted one of his personal lawyers, Michael Cohen, in a separate investigation. "This isn't any different, it's just because of the timing", she said on CNN's "Erin Burnett OutFront".
The biggest change, Cobb's departure removes the strongest voice the president heard on a daily basis not to fire Mueller.
Other reporting indicates that while the Trump legal team is hesitant to have the president sit down for an interview, Mueller is willing to issue a subpoena for his testimony, if necessary. He also said it is "an open question" if Mueller could compel Trump to testify.