Petrie's role at the club has become a running sore for some of the relegated Edinburgh side's disgruntled supporters but in theory at least his sole contribution to the recruitment of the club's seventh permanent manager in the last eight years will simply be conferring the blessing of the board on whoever his newly-appointed chief executive recommends.
A list of about 40 applicants and suggestions has been whittled down to just a handful of names, and with erstwhile championship rivals Hearts and Rangers stealing a march on player recruitment, ideally the new manager will be in place by the end of the week.
Bookmakers regard Dumbarton's Ian Murray, Owen Coyle and Motherwell boss Stuart McCall as favourites for the job, though whether Dempster's former colleague could be persuaded to leave Fir Park is unclear.
"My whole attention is focused on it," said Dempster. "We've had over 40 applications and there are individuals we've added to that list, so I'll take the long list and make it a bit shorter. I'm finalising that now and my plan is to make some calls and get out over the weekend and have some conversations. I'll be doing it myself, but I'll maybe be asking another board member to attend. If you want to ask the question 'will that board member be Rod Petrie?' the answer to that is 'no'.
"It's important to hire the right person and I need to take that responsibility on my own. It's important to take someone else with me though, because I don't know everything about the football club. There is a process, that's what happens at most football clubs. I'll take a strong recommendation to the board, and I would be very disappointed if they don't support that."
Assuming this lack of boardroom interference comes to pass, as troubled as they seem right now, Hibs are actually an enviable blank canvas for the former Motherwell chief executive. There is a need to assemble a football department, rather than just appoint an individual.
"We don't have a goalkeeping coach, a sports scientist, or an analyst; these are things we want to put in place," said Dempster.
Further imported expertise comes in the form of George Craig, formerly managing director at Falkirk, who left a post at the SFA last week to become head of football operations, which will see him oversee the functions of the club's academy and a tie-in with Spartans FC.
That the role of goalkeeping coach should be included on the list of vacancies is particularly interesting, considering the club appear to have two on their books. Steve Marsella, the club's chief scout who unearthed many of Terry Butcher's gems at Inverness Caledonian Thistle, doubled up in that role last season, a move which saw existing coach Scott Thomson unceremoniously shunted down the pecking order.
While the future of Thomson remains unclear, Dempster has spoken twice with Marsella and will speak to him again this week. With a bit of tinkering in his job description, she feels he could yet have a key role to play.
"Steve is still an employee, but I'm looking at that specific position in terms of resource," said Dempster. "He was obviously brought in to look after the first team but what we need to do is have a more holistic perspective and look at how you get to the first team as well.
"We need to focus on recruitment generally and that means from the academy up. I see him as a valuable part of the club moving forward, although he is aware that like everyone else in football what happens is dependent on the new manager that comes in. That is just the nature of the business we are in."
As for the players, the new manager will have 15 at his disposal, none of them goalkeepers, with contracted senior players such as Liam Craig and Scott Robertson thought to have been told they are free to find a new club. While the new manager may have his own ideas, the rest are expected back for the start of pre-season on June 23.
Season tickets are another worry, with sales noticeably lower than this time last year. Dempster feels confident discerning fans will sign up when they see the manager and players arriving.
As successful as many of her appointments at Motherwell have proved, the job specification at Easter Road is different to Lanarkshire. "There's a different job to be done at this club. I want someone who is desperate to get this job and desperate to prove themselves.
"You can maybe read into that that it is a young manager but it might be someone who has been out the game for a little bit, someone who has been a No 2, or someone who has been working as a coach. The important thing is the skill set."
Billy Dodds: Page 20