Newcastle United assistant boss Ian Cathro and St Johnstone manager Tommy Wright have distanced themselves from the vacant post at Dundee United.
Cathro, who was a youth coach at Tannadice, says he is "entirely focused" on his role at Newcastle and has "not applied" for the United job.
Meanwhile, Wright said: "I'm happy here. That's why I signed my new deal."
Raith Rovers manager Ray McKinnon is thought to be United's main target after Mixu Paatelainen's departure.
But McKinnon has stressed he is concentrating on his job with the Kirkcaldy outfit, who could yet be promoted to the top flight after beating Hibernian 1-0 on Wednesday in the first leg of their quarter-final play-off.
Cathro, 29, who was head of United's youth academy at the age of 22, was assistant manager to Nuno Espirito Santo at Rio Ave in Portugal and Spanish club Valencia before joining Newcastle last summer.
He survived the March departure of Steve McClaren to work under Rafael Benitez.
The bookmakers have installed Wright as second favourite despite Saints having rebuffed United's approach for the Northern Irishman before Paatelainen's appointment in October.
Wright, who signed a new three-year contract immediately after that approach, said: "I can only see one name mentioned.
"I don't know why my name would be mentioned when I've just signed a three-year contract. We are still in the Premiership, so I am puzzled by it all."
St Johnstone presently sit fourth in the Premiership - their fifth consecutive top-six finish - and Wright has been promised a larger budget next season.
"With the success we've had over the last three years, I feel the time is right to make more money available and try to bring a wee bit more quality in so we can try to compete with the other clubs around us," said 52-year-old Wright.
'We all want to work at the highest level' - McKinnon
McKinnon has earned plaudits for Rovers' fourth-place finish in the Championship a year after arriving from Brechin City.
However, asked about the United job, he told BBC Scotland: "I haven't given it any consideration at all.
"The whole week has been about focusing on this game last night and I am solely focused in trying to get Raith Rovers to the Premiership."
McKinnon has had a great affection for United since he was a boy and says the size of the club dictates it should not be facing life in the Championship.
"They are a massive club," said the Dundee-born boss, named as Championship manager of the month for April. "They are one of the top five or six clubs in Scotland and one of the best supported as well.
"Both my sons are United fans, so I do follow their progress and it is sad to see where they are.
"A club that size shouldn't be in that position. Just like Hibs, these are big, big clubs and we need them in the Premier League."
McKinnon would not be drawn on any move for him to take over at Tannadice but reiterated his ambitions as a manager.
"We all want to work at the highest level," he added. "If you are not ambitious then you are going to stagnate.
"I have that drive, but at this moment my ambitions are solely on Raith Rovers."