The White House legal team reportedly torpedoed the meeting after hearing the planned scope of the interview.
Trump allegedly went "ballistic" and was "not under control" during the practice interview.
"Imagine your lawyer telling you 'you're disabled' and you can't testify because you can't tell the truth. You just make things up," Woodward said.
A new excerpt from the book obtained Wednesday by The Atlantic showed that numerous questions posed to the president by Dowd pertained to Flynn's conversations with a former Russian ambassador, Sergey Kislyak.
"The law firm of Larry, Mo and Curly, and of counsel Rudy, can't actually find out what the truth is," Scarborough said of Trump's legal team.
The president's lawyers are concerned he could face charges of lying to special counsel.
Cobb also echoed the call by Jay Sekulow and others for a second special counsel.
Many view the tweet as an admission that Trump was aware Flynn had lied to federal agents when he fired him.
John Dowd's claim he wrote the post on Trump's Twitter page "makes no sense," say legal experts.