No official word came out of Dens Park on Friday but Farningham was working very much on an interim basis with no assurances that he will be in charge at Celtic Park. Dundee chief executive Scot Gardiner was away from the ground on Friday amid reports the club were interviewing three candidates.
Former Dundee players John Brown and James Grady have been linked with the job along with former St Johnstone captain Jody Morris. Former St Mirren and Queen of the South boss Gus MacPherson and ex-Aberdeen manager Jimmy Calderwood are also reported to be in the frame.
Calderwood told BBC Radio Scotland's Sportsound on Friday night that his representatives had been in contact with the club.
"You have people working for you," he said. "They phone you up and see if you are interested and then they go and talk to the directors. The thing with Dundee, a lot of people on the board are supporters. That can be a good thing but it can also be a bad thing."
Calderwood added: "Looking at years gone by, it's a fantastic club and probably I would say after the top five - the two Glasgow teams, the Edinburgh teams and Aberdeen - I would say they are the next biggest team in Scotland, potential wise.
"They have a fantastic support. I remember being at Ross County when they were trying to stay in the league and they must have taken 2,500 fans up there. It was unbelievable."
Smith earlier revealed his hurt at being sacked by the club he had been at for a total of 17 years as player, captain and manager. Smith, who was sacked on Wednesday, told the Scottish Sun: "The people at Dundee are like family to me. The club has been a huge part of my life - I've been there 17 years and we have been through so much together.
"Saying goodbye was tough. To be no longer part of that is very difficult."
The players were on Friday told not to speak to the media after defender Davide Grassi criticised the timing of the board's decision. Dundee are 15 points adrift in the SPL but face city rivals United in the William Hill Scottish Cup quarter-finals a week on Sunday.
- Sports & Recreation
- Jimmy Calderwood