Chief executive Scot Gardiner says the club have been "swamped with applications" for the vacant position following the 39-year-old's departure from Dens Park
Dundee have parted company with manager Barry Smith, with the Scottish Premier League strugglers 15 points adrift at the bottom of the table.
After earning promotion from the First Division last season, Dundee have suffered in the top flight under Smith’s stewardship - losing 18 of their 26 games so far this term.
And, despite the club booking their place in the Scottish Cup quarter-finals against rivals Dundee United, the Tayside club have decided to look for new guidance - with chief executive Scot Gardiner insisting the club have been inundated with applications.
"Dundee FC today announced that they have parted company with manager Barry Smith with immediate effect," an official club statement read.
"Until matters regarding this have been formally concluded, no further statement will be made."
“There are two situations,” Gardiner told BBC Scotland.
"There's a possible interim manager that we would appoint and there's also the potential which could be a full blown managerial appointment.
"I've been absolutely swamped with applications direct from managers and their agents."
Assistant manager Ray Farnigham is to take charge of first-team affairs for Sunday's match against Celtic in Glasgow.