That means caretaker Neil Young - who secured a fine 1-1 draw at leaders Wrexham on Saturday in his only game at the helm - will take charge this weekend.
Town host Ebbsfleet United looking to move further away from the National League’s bottom four.
They parted company with manager Billy Heath, who took them up last season via the National League North play-offs.
Chairman David Bosomworth says interviews are ongoing and told the Halifax Courier that the Shaymen will be in Young’s capable hands on Saturday.
“We have a couple more to see,” said Bosomworth in an interview with his local newspaper. “It’s progressing well but we’ve seen some good candidates.
“Quite a few of them could do the job but we’re trying to see who will fit in with the type of job we have going forward.
“We want to appoint someone as soon as possible. We’re looking at all sorts of candidates but we want the person that ticks the most boxes.”
Young, the former Chester and Altrincham manager, praised his players for the valiant draw at the Racecourse.
But he is keen not to let standards slip. Following their home game with Ebbsfleet on Saturday, Halifax then face Hartlepool United at the Shay on Tuesday night.
“It’s a big period in the club’s season and we need to build on Saturday,” said the caretaker, who has been out of management since leaving Alty.