Queen of the South chairman David Rae has refused Dundee permission to speak to the club's manager Gordon Chisholm.
Dundee are seeking a successor to Alex Rae, who was sacked last week. But Rae said Chisholm told him he was happy to remain at Palmerston.
"I think going to Dundee wouldn't be a step up for our manager," said Rae.
Division Two table-toppers Brechin City have also rebuffed an approach from the Dens Park club to talk to their manager Michael O'Neill.
The Dark Blues have already been denied permission to speak to Airdrie United boss Kenny Black.
Chisholm, whose side currently lead the First Division, said last week that he was flattered to be linked with Dundee, while O'Neill had also expressed an interest in the vacancy.
"Had it been the SPL, the Premiership or even the Championship south of the border, then I would have considered giving permission," added Queens chairman Rae.
Meanwhile, Brechin issued a statement saying: "We have an open and honest relationship with our manager, and whilst he has ambitions to further his football career, he is currently fully committed to Brechin City and we have no intention of losing him."
Rae was sacked by the First Division club last week, with his assistant David Farrell taking charge of first-team affairs for Saturday's 2-0 defeat by Morton.
The defeat was Dundee's 10th match without a win and left them ninth in the First Division table, having finished second in the league last season.
"We have got five or six people that we have whittled down from 20-odd," said Dundee chief executive Dave MacKinnon.
"It is pretty imperative we get someone in pretty quickly."
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Former Northern Ireland international O'Neill spent much of his playing career in Scotland, including a spell with Dundee's city rivals Dundee United.
"I'm sure that the Dundee fans would rather one of their old favourites was put in the position of manager," O'Neill told BBC Sport.
"But in management, if you can get results, it doesn't really matter what your past is and that would be my aim if I was to go into a job like that."
Craig Brown and Billy Davies have been linked with the post but are unlikely to be tempted by First Division wages, while Jocky Scott, who has twice been in charge at Dens Park before, is being tipped to return.
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