Mr. Huckabee will tape the interview with Mr. Romney on Friday, and it will be broadcast on his Fox News show, which airs on Saturday and Sunday evenings at 8 p.m. Eastern Standard Time. Promos for the interview are set to broadcast Thursday afternoon on the network.

The men have had a tense relationship since 2008, when a surprise victory in the Iowa caucuses by Mr. Huckabee, a former governor of Arkansas, upended a carefully designed plan by Mr. Romney, a former governor of Massachusetts, to win the state that year.