Both players missed the 4-1 defeat by East Midlands rivals Leicester at the King Power Stadium on Saturday evening.
Bryson was absent with a knee injury sustained in the home draw with Cardiff, while Roberts limped off in the same game with a calf problem.
It was only the second match Bryson has missed this season. The Scottish midfielder sat out the 3-0 Championship defeat at Peterborough in October.
"He will do everything he can and we will do everything we can to get him right for Leeds," said Rams manager Nigel Clough after the Leicester loss.
"We miss him when he doesn't play. We miss his energy, his closing down and him getting a tackle in. He has missed two games, against Leicester and Peterborough, and we have lost them both by a three-goal margin."
Roberts is less likely to make it in time for the Leeds game. The 34-year-old's left-back slot against Leicester was filled by James O'Connor.
Clough added: "We missed Craig Bryson but I thought we missed Gareth Roberts more, and we'll have to see what happens with his this week.
"Jimmy O'Connor struggled at times at left-back. Right-back or centre-half is Jimmy's position, so we were asking him to play out of position."
Derby forward Jamie Ward, meanwhile, has had an injection to try and aid his recovery from a troublesome hamstring injury.
Ward has missed the Rams' last 11 matches since sustaining the problem during the 1-0 win over east midlands rivals Nottingham Forest at the City Ground at the end of September.
Clough said: "We'll see how the hamstring settles down following the injection. It's just time and patience with Jamie.
"His chances of being ready for Saturday? It depends how the hamstring settles down this week."