Portsmouth chief executive David Lampitt says it is important the club's next boss has Championship experience as first-team coach Guy Whittingham ruled himself out of the running.
Pompey have begun their search for a new manager following Steve Cotterill's exit to Nottingham Forest on Friday.
Lampitt says they have already drawn up a shortlist and knowledge of English football's second tier is vital.
"Championship experience is important," Lampitt told BBC Radio Solent.
Whittingham and fellow first-team coach Stuart Gray took charge of Pompey for Saturday's 2-0 victory over Barnsley to help move the South Coast side away from the bottom three.
But, when asked if he wanted to take over from Cotterill, Whittingham told BBC South: "No, not at all.
"We just want to steer the ship until someone arrives to take over.
"It's up to the owners who they bring in. We just want to give them enough time to find the right person."
Lampitt says Pompey will not be rushed into naming a replacement for Cotterill and have been inundated with interested suitors.
"It is important for us to get the appointment right and not to rush it at the expense of getting the right person in," added Lampitt.
"So there will not be a knee-jerk reaction and we will not appoint someone immediately just for the sake of having somebody here. We want to make sure we get the right person in.
"I've spoken to the owners, we've got a list of criteria that we think is important for the new manager and the process of drawing up a shortlist and sorting our priorities is well under way.
"It is fair to say my phone has been busy and I've had phone calls, text messages and emails from football managers and their agents, advisors, lawyers and friends.
"It's a positive indication about the level of interest there is and rightly so.
"This is an opportunity for someone to manage a fantastic football club and come in and match the ambitions of the club and the new owners and take the club forward."