Given the president’s sentiments, he might view any link to Mr. Mueller with suspicion, including Ms. Gorelick’s representation of Mr. Kushner, according to one person who has been contacted about the matter. An official close to the president disputed that, saying Mr. Trump is pleased with Ms. Gorelick’s representation of his son-in-law.

Although Ms. Gorelick is a well-known lawyer who has often handled complex cases involving government investigations — and some of her colleagues on her team are noted courtroom litigators — she is also not primarily a trial lawyer.

In contrast, people within Mr. Kushner’s circle recently reached out to some courtroom litigators about possibly joining his legal team. Among the lawyers contacted, one person said, was Abbe D. Lowell, a prominent trial lawyer whose previous clients include Jack Abramoff, the powerful Republican lobbyist, in a corruption scandal that shook Washington in 2005. Mr. Lowell is currently defending Senator Robert Menendez, Democrat of New Jersey, against federal corruption charges.