But chief executive Dave MacKinnon expects two more knockbacks after Airdrie chairman Jim Ballantyne angrily rejected an approach for Kenny Black.
Dundee's need for an appointment grew after yesterday's 2-0 defeat by bottom club Morton left them in ninth place in the Irn-Bru First Division.
The Dens Park club have also been linked with Queen of the South manager Gordon Chisholm and Brechin's Michael O'Neill, but MacKinnon is not optimistic about prising anyone away from a job.
Chisholm continued to bolster his reputation as Queens remained top with a 2-0 win at Ross County thanks to strikes from Michael McGowan and Stephen Dobbie in either half.
St Johnstone defender Stuart McCaffrey netted in a 3-0 win over Partick but claimed the high winds should have forced a postponement.
Clyde boss John Brown had the same opinion after three of his players needed hospital treatment following their 2-1 win over Livingston amid wet and windy weather.
Brechin manager O'Neill was delighted with his side's character as Darren Smith earned the Second Division leaders a 2-1 win over Queen's Park.