Dundee have released Adil Nabi, while Andy Boyle and Calvin Miller will return to their parent clubs.
Defender Boyle, 27, joined on loan from Preston and left-back and winger Miller, 20, arrived from Celtic.
English midfielder Nabi, 24, signed a short-term contract at Dens Park after leaving Peterborough but will not be offered a new deal by Dundee.
Jim McIntyre's side are two points adrift at the bottom of the Scottish Premiership.
They return to action after the winter break against Queen of the South in the Scottish Cup on 19 January and resume their league campaign against Hearts four days later.
McIntyre said on Thursday midfielder Lewis Spence and strikers Jean Alassane Mendy and Marcus Haber are free to leave Dundee, with Haber currently on loan at Falkirk.
And Kharl Madianga, Sofien Moussa and Elton Ngwatala are also expected to depart Dens Park.
Speaking after Saturday's 2-0 home defeat by St Johnstone, McIntyre told BBC Scotland: "Clearly, we need to strengthen. It's as clear as day."