The pair left Dens Park on Friday lunchtime after being told the news by Bryan Jackson of PKF.
Jackson, who was appointed on Thursday after the club admitted defeat in their attempts to pay a £365,000 tax bill, was this informing the players which of them would also lose their jobs on Friday afternoon.
Chisholm and Dodds had only been at the club since March, when they were persuaded to leave Queen of the South after Jocky Scott was sacked while sitting on top of the Irn-Bru First Division.
Jackson will explain his cutbacks at a Dens Park media conference scheduled for 2.30pm.
The administrator, who has presided over similar situations at Clydebank and Motherwell, will attempt to steer the club through the coming weeks while new investment is sought.
With debts reportedly approaching £2million, Dundee continue to rely on director Calum Melville for funding.
It is understood Melville has paid the first instalment of the £200,000 he has agreed to pledge to the club to see them through the administration period. Three more instalments of £50,000 will be paid between now and December 31.
Melville said: "I know a number of people have come forward to pledge funds, which is fantastic.
"I`m hoping if there is anyone else out there who can help the club financially, they will come forward and do so."
Source: PA
Source: PA