The Minstermen travel to Stockport County on January 19 - their next National League North fixture with the side without a game this weekend.
York are looking for a new boss having parted with Sam Collins on Saturday night.
City are well off the play-off pace after a poor season which has seen the club stranded in the lower half of the table.
Dave Penney is in caretaker charge but if all goes to plan he will not have to take control of a game.
Managing director Steve Kilmartin has given an interview to the York Press and he says fans can be excited about the calibre of men throwing their hat into the ring.
“There are already a number of applications and there are some very credible applications," Kilmartin said.
"We have had a considerable flurry of people interested in this position because of it being York City, which in many ways is extremely reassuring.
"We are preparing a list with the intention of interviewing some of these people later in the week.
"Things are moving forward quickly. There are names in there that would be well-received by the fan base, by people who do follow football."
Kilmartin added: "We have Stockport a week on Saturday and we would like to make an appointment before then if possible.”