WASHINGTON — Bill Shine, a former Fox News executive who was close to Roger E. Ailes, the network’s ousted chairman, is expected to be offered the job of White House communications director, according to four people familiar with the decision.

Mr. Shine, who was forced out as co-president at Fox News last May for his handling of sexual harassment scandals at the network, has met with President Trump in recent weeks about taking the West Wing communications job, which has been vacant since Hope Hicks left the job in March.

Four people familiar with the decision said it was likely to be announced and that the president had offered him the job. But the move has not been finalized, in part because of the president’s mercurial decision-making process and also because of Mr. Shine’s reluctance to walk into a chaotic West Wing.

As recently as a month ago, Mr. Shine didn’t want the job, according to a person familiar with his thinking. The former television executive was reluctant to deal with all the scrutiny, part of which could focus on his own connection to the sexual harassment scandal at Fox News, the person said.