West Brom boss Alan Irvine has admitted he is keen to add another striker this summer after already signing Brown Ideye.
Swansea boss Garry Monk is adamant that only an “astronomical” bid could prise Wilfried Bony away from the club.
The Reds, who are currently bottom of the Championship, are looking for a replacement for Keith Hill, who they sacked last week following a run of one win in 14 games.
Former Nottingham Forest boss Sean O'Driscoll is favourite for the position and was believed to have met with the Barnsley board on Thursday, but Friday's announcement now casts doubt over whether he join the Oakwell club.
"The board of Barnsley FC have drawn up a shortlist of applicants for the vacant first-team manager's position and the interview process has commenced," the club said.
"The board will seriously assess every aspect of the character they want to bring into the football club before making a decision.
"It has been said that it is a tradition of Barnsley Football Club to change the manager often, whereas reality suggests prior to Keith Hill's departure there had been only one managerial dismissal in the past six years.
"The board has stated it is imperative that, as a club, they realign themselves with the supporters.
"Barnsley Football Club need to become more involved in the community - an area in which it appears to have taken a backwards step over the past couple of years.
"The board are hopeful of making an appointment prior to the Leeds United fixture on January 12."
Hill's assistant David Flitcroft is in temporary charge and could be in the frame, though he admitted on Friday he had not applied for the job.
"It has been difficult, frustrating and there has been a lot of hurt and some anger," said the 38-year-old of his feelings on the last week's events.
"On Sunday morning I woke up and wanted to fight for Barnsley football club and the group of players that we have assembled.
"I do believe there is a fight in there which I want to continue with and I think the lads want to fight with me.
"I have turned the sacking into a positive and I really want to do well for this football club.
"I was as close as you could imagine to leaving, there is a reason why I have not left.
"I don't know what the future holds for me, but I know that as long as I am here I will give all I've got to Barnsley football club."