Former England manager Kevin Keegan has been approached by Hearts as they continue their search for a new boss, BBC Sport understands.
It is believed that Keegan was on Hearts' shorlist in the summer before the appointment of George Burley.
The Edinburgh club now want to talk again to the former Manchester City and Newcastle United boss.
Sir Bobby Robson is still in the running, but Claudio Ranieri has priced himself out of the frame.
And, despite newspaper speculation linking Ottmar Hitzfeld with the job, it is believed that the former Borussia Dortmund coach is not interested, while former Parma boss Nevio Scala has not been approached.
Hearts' unbeaten league run was ended by Hibernian in John McGlynn's third game as caretaker boss on Saturday.
But chief executive Phil Anderton told BBC Radio Five Live: "We are going to take the appropriate time to reach our long-term aspirations."
Keegan resigned from Manchester City in March and it was thought at the time that it would be his last managerial appointment.
Fellow former England boss Robson turned down the Hearts job in the summer for personal reasons before the appointment of George Burley but has held new talks.
It appears that the 73-year-old wants to be coach, while it is thought that majority shareholder Vladimir Romanov sees him more as a director of football overseeing another new man to train and pick the team.
"It would fantastic if someone like Sir Bobby could come and join us at this club," said Anderton.
"Sir Bobby Robson is a quality manager with a superb track record and we are very impressed with his abilities.
"There's more people applying than the summer of a higher level of experience.
"The club is so much more in the media spotlight and we are top of the league. People are looking at us and wanting to be part of it.
"We are looking for the quality and the finance comes next.
"We are looking for someone who has coached at the highest level and someone capable of taking the club into Europe.
"I would hope we will have someone this week, but that is all down to negotiation."
Former Chelsea boss Ranieri said that the prospect of becoming Hearts' new manager was an attractive one after meeting with the club.
"I think that could be a good project," said 53-year-old Ranieri, who left Valencia in February.
"The first meeting is important and it was good.
"I think Mr Romanov wants to do something very important and I'm looking for a good project."
Hungary coach Lothar Matthaus is thought to be interested in the post, while Hearts are also keen to talk to sacked Republic of Ireland boss Brian Kerr.
Scala was interviewed during the summer but confirmed: "I have not been contacted. I have said before that the job interests me, but they know my phone number."
Burley parted company with the SPL leaders after being reportedly concerned at Romanov's interference with team affairs.