Alex Dyer will take charge of Kilmarnock until the winter break, but is not "on trial" for the role permanently, according to head of football operations James Fowler.
Dyer says he will not apply for the job but if the board offer it to him he would then consider the position.
Fowler insists no candidates have been identified to succeed Angelo Alessio, who was sacked on Tuesday.
The Italian's exit was put down to a variety of reasons, not just results.
Alessio was recruited in the summer after Steve Clarke left to become Scotland head coach but the former Juventus coach lasted just 22 games.
Dyer, 54, joined the Ayrshire club in 2017 as Clarke's assistant and is also part of his backroom team with the national side.
"Of course, I would love to be a number one at one point but at this present time I have this job which I want to do well," said the Englishman.
"If the club turned round and said 'do you want the job?' then I will make a decision then, but I will not be putting my name down and saying I want the job."
Fowler, formerly manager of Queen of the South and an assistant at St Mirren and Sunderland, has ruled himself out of the running.
"We don't want to put Alex in a position where he feels that it's a trial or that it's necessarily how he does in these games," said the ex-Killie midfielder.
"We've asked him to do the job in the short term and we'll deal with that probably closer to January."
Fowler, who took up his post last month, conceded the next appointment is unlikely to be as leftfield as Alessio's.
"I think potentially British football is maybe something you look at, experience within that," he said.
"It doesn't necessarily have to be a British coach. It's maybe someone with experience of English football. We've got, within the building, a good knowledge of Scottish football, so just in terms of player recruitment it obviously helps.
"Somebody that maybe knows the club and knows what they're coming into, at the level that they're at as well, it might be obviously beneficial for the club moving forward."
'The club felt they wanted to make a change'
Fowler went on to deny he had been approached by players unhappy with Alessio's methods.
"I just think the club felt they wanted to make a change," he said. "Obviously people looking at the league table might say 'he's in a decent position, why's that the case?'
"All managers will get monitored in terms of results on the pitch, performances, how they deal with the group as well.
"If results or performances haven't been great and you are getting a good spirit, and performances are there and you are maybe just not picking up results, from a board point of view or club point of view, we have looked at that over the last month to six weeks and that has probably been a factor."