Hearts have received more than 20 applications for the job of manager, with Sir Bobby Robson and Nevio Scala two of those set to be interviewed.
BBC Sport understands that discussions will begin with potential successors to George Burley within 48 hours.
Robson turned down the job in the summer but has renewed his interest, while Scala was among the leading candidates before Burley's appointment.
Hungary coach Lothar Matthaus is also thought to be interested in the post.
Interim boss John McGlynn could also be interested in the vacancy but is unlikely to have the public persona demanded by majority shareholder Vladimir Romanov.
Former Kaunas head coach Valdas Ivanauskas has been helping McGlynn with training, but Hearts have stressed that Romanov's countryman will not be on their shortlist.
Burley parted company with the Scottish Premier League leaders on Friday following a disagreement with the Lithuanian businessman.
The former Ayr, Ipswich and Derby boss had complained of Romanov's interference in team affairs before leaving after just 113 days in charge.
But Romanov spokesman Charlie Mann has attempted to reassure potential candidates.
"Vladimir Romanov does not pick or select the team," he said.
"George Burley was the manager and had the final say in the selection of the team."
The 72-year-old Robson, who has already said that he would not tolerate meddling from chairmen or owners, says changed circumstances from the summer mean he could now accept the job.
Hearts chief executive Phil Anderton said: "He decided he could not join at that time and we understood that.
"We have kept in touch since then and he is somebody we respect for obvious reasons.
"I would be delighted to have a chat, even just to say 'hello' because who knows whether, in reality, this is something he would consider.
"So we are not getting carried away about speculation on that one."
Nevio Scala is keen on Hearts
Bookmakers' favourite Robson will be in Edinburgh this week to attend the funeral of his friend and former Fulham and England team-mate Johnny Haynes.
And the former England boss reiterated his belief over the weekend that the Hearts position is "an attractive job" and that he left Romanov "on good terms" after their previous talks.
But the former Ipswich, Newcastle, Barcelona and PSV Eindhoven manager said: "I have never stood for any interference from my chairman.
"At all the clubs I've been at, the selection policy has been down to me."
Former Parma and Borussia Dortmund boss Scala, who also held talks with Hearts in the summer, says he would be willing to hold further discussions with the club.
"I will be very glad to talk if Mr Romanov picks up the phone," said the 57-year-old Italian.