Mr. Shine, who was forced out as co-president at Fox 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.

The move has not been finalized, but two people familiar with the decision said it was likely to be announced and that the president had offered him he job.

Officials at the White House are aware that they will face blowback for appointing someone so closely tied to Mr. Ailes and the culture of harassment toward women at Fox News. But they said Wednesday that they believe they can weather it.