Job would put George Conway at forefront defending immigration executive order and other lawsuits against Trump administration

George Conway accompanied his wife, Kellyanne Conway, to a function in Washington in January.

WASHINGTON—George Conway, the husband of senior White House adviser Kellyanne Conway, is set to be nominated to run the Justice Department’s civil division, according to people familiar with the matter, a job that would put him at the forefront defending the controversial immigration executive order and other lawsuits against the Trump administration.

Mr. Conway, a partner at Wall Street law firm Wachtell, Lipton, Rosen & Katz, had also been in the running for other jobs at the Justice Department.

He has worked on major securities law cases and deal litigation, according to his law firm biography.

Mr. Conway didn’t immediately respond to a request for comment. The Justice Department declined to comment.

Ms. Conway, a longtime Republican pollster who helped turn around Donald Trump’s Republican presidential campaign, has been a common presence on television defending Mr. Trump. She took on a senior role in the campaign last summer, when Mr. Trump trailed Democratic candidate Hillary Clinton by 16 percentage points in a Wall Street Journal/NBC poll.

This week Ms. Conway was criticized for comments she made defending Mr. Trump’s unsubstantiated claims that he was wiretapped by his predecessor. A bipartisan statement from the Senate Intelligence Committee leaders said Thursday they have seen no evidence for such a claim.

Mr. Conway’s nomination is set to come as the Justice Department prepares appeals of rulings that blocked Mr. Trump’s revised executive order on immigration. That dispute could arrive soon at the Supreme Court.

Judges in Hawaii and Maryland halted Mr. Trump’s latest effort this week after finding he likely engaged in religious discrimination when he sought to bar U.S. entry for people from six Muslim-majority nations, a move the White House says could help fight terrorism.

Among Mr. Conway’s first tasks—if confirmed soon by the Senate—would be to manage that defense.

Mr. Trump’s revised travel restrictions made several concessions from his original Jan. 27 executive order in response to negative court rulings. That he was blocked anyway is increasing friction between the White House and the courts, and it sets the stage for appellate proceedings that could have even higher stakes than during the initial round of litigation a month ago.