Interim Hearts boss John McGlynn has voiced concern that any British manager can work under the watchful eye of majority shareholder Vladimir Romanov.
George Burley left the club last week having previously complained about interference in team selection.
And McGlynn said: "At teams like Real Madrid and Barcelona, there is maybe a bit more interference and maybe we're not used to that in Britain.
"Can any manager work in those circumstances? Only time will tell."
McGlynn is preparing to be in charge on Wednesday against Kilmarnock and on Saturday against Hibernian as he does not expect Hearts to rush a decision.
He is in his third spell as caretaker manager and faces a nervous wait to see whether he will be retained whoever decides he can work under Romanov.
But chief executive Phil Anderton has played down suggestions that Romanov interferes with team selection.
"The final decision about who goes into the team rests with the manager," he said.
Anderton said he would not break the confidentiality agreement with Burley about the reasons for his departure.
But he said: "Let's be clear on this, I have views on the team, supporters have views about the team and Mr Romanov has views about the team, but the manager picks the team."
Romanov had signed some players of his own choice for the club.
But Anderton thought that any manager would be pleased to have been given the likes of European Championship winning full-back Takis Fyssas.
Anderton also explained that Valdas Ivanauskas was helping with coaching but was not a candidate for the job.
Former Kaunas and Vilnius manager Ivanauskas has been helping McGlynn since Burley left before Saturday's win over Dunfermline Athletic after a row with Romanov.
"He is the assistant manager and has been involved for a number of months now," said Anderton.
"He has just returned after working with the Lithuanian national team but will not be on our shortlist."
Romanov said he would not be rushed into a decision.
"I have always said we will pay for quality and professionalism and that does not mean taking the first individual available," said the Lithuanian businessman.
Romanov said he was disappointed that a way could not be found to keep Burley at Tynecastle but that the search for a new manager was already making significant progress.
"I would like to place on record my thanks to George Burley for his input over the past four months," he said.
"However, we will not be derailed from our ambition to deliver to the fans and the city of Edinburgh a club which is regularly competing at the highest levels of football in Scotland and Europe.
"I want the club to be winning the Scottish Premier League title on a regular basis as well as playing top-quality football in the Champions League.
"I have kept all my promises to Hearts fans and want them to know that they and the club can look forward to further investment on and off the field.
"Our minds are not closed to any candidate or approach to the job, but the person will be of the highest possible quality and able to deliver the success that the club and all Hearts fans deserve."