Dundee hope to appoint an interim manager in the next 24 hours following Monday's sacking of Paul Hartley.
The Dens Park club, whose side sit second bottom in the Scottish Premiership, has drawn up a shortlist.
And managing director John Nelms wants to have reached agreement with the preferred choice by Wednesday evening.
Nelms told BBC Scotland that the ideal candidate is a British manager and preferably someone who knows the club and the Premiership well.
The new manager is likely to be appointed until the end of the season, tasked with keeping the club in the top-flight, before any discussions about a longer-term contract are held.
Hartley's assistant, Gerry McCabe, and youth coach Jimmy Boyle have taken charge of the first team in the meantime.
Dundee's next fixture is away to Motherwell, who are one place and two points above the Dark Blues, on 29 April.
Hartley was sacked after a run of seven straight defeats, with Hamilton Academical climbing above his side after Saturday's 2-0 win at Dens Park.
Alex Rae, who was Dundee manager for two years in the second tier before being sacked in 2008, has told BBC Scotland he is interested in a return to the Dark Blues.
Rae, who was dismissed by St Mirren in September after a poor start to their Championship campaign, expects that former Hibernian manager Alan Stubbs would be a strong candidate to take over at Dens Park.
Stubbs left Hibs in the summer, after they won the Scottish Cup, to join Rotherham United but was himself sacked by the English Championship club in October.
Former Dundee forward Fabrizio Ravanelli, who managed French side Ajaccio in 2013, has told the Scottish Sun that he would be interested in the Dens vacancy.