Mr. McGahn also told White House officials that Mr. Trump would not follow through on the dismissal on his own.
He has been involved in nearly every key decision Mr. Trump has made — like the firing of the former F.B.I. director — that is being scrutinized by Mr. Mueller.
Mr. McGahn was also concerned that firing the special counsel would incite more questions about whether the White House was trying to obstruct the Russia investigation.
Mr. Trump has significantly ratcheted back his criticisms of Mr. Mueller since he hired Mr. Cobb for his legal team in July.
He advised Mr. Trump that he had nothing to gain from combat with Mr. Mueller, a highly respected former prosecutor and F.B.I. director who has subpoena power as special counsel.
The White House has denied nearly a dozen times since June that Mr. Trump was considering firing Mr. Mueller.
Last month, as Republicans were increasing their attacks on the special counsel, Mr. Trump said in an interview with The Times that he believed Mr. Mueller was going to treat him fairly. »