The Robins, meanwhile, will need to pick themselves up after losing 4-0 to Barnsley and Portsmouth in their last two games.
Match preview
Derby had lost once in 14 league games prior to Saturday's away meeting with Barnsley, which proved to be a forgettable afternoon.
David McGoldrick pulled a goal back after Devante Cole and Adam Phillips had given the Tykes a 2-0 lead, but Cole scored his second goal in first half stoppage time to restore Barnsley's two-goal advantage.
While the Rams were unable to mount a fightback in the second half, Barnsley added to their tally in injury time through Luke Thomas to condemn Derby to a 4-1 defeat.
Although Paul Warne's side will be downbeat following Saturday's encounter, they remain in the playoffs and hold a four-point advantage over seventh-placed Wycombe Wanderers.
The Rams are currently unbeaten in 10 league games, and after winning eight of those matches they may be confident that they can claim three points on Tuesday.
Cheltenham will be hoping for an upturn in fortunes, after experiencing three disappointing results in the space of a week.
After being thrashed 4-0 by Barnsley, the Robins took Plymouth Argyle to penalties in their EFL Trophy semi-final, but three missed spot-kicks ended their Wembley dreams.
They were ultimately unable to pick themselves up from their semi-final disappointment, suffering another 4-0 defeat in their away meeting with Portsmouth on Saturday.
Having won just one of their last 10 league games, Cheltenham are languishing in 19th place - two points above the relegation zone.
While Wade Elliott will be concerned by his side's recent defensive displays, he will also be looking for an improvement in the final third, as Cheltenham are the lowest scorers in the division with 25 goals from 32 games.
Derby County League One form:
W
W
L
D
W
L
Derby County form (all competitions):
L
W
L
D
W
L
Cheltenham Town League One form:
D
L
D
W
L
L
Cheltenham Town form (all competitions):
L
D
W
L
L
L
Team News
Derby are still expected to be without the services of James Chester and Max Bird, who are recovering from injury issues.
After featuring as a second half substitute against Barnsley, Lewis Dobbin could be brought into the starting lineup on Tuesday.
McGoldrick will continue to lead the line for the Rams, and the forward will be looking to find the net in a third consecutive game.
As for the visitors, may be unable to call upon Elkan Baggott, Lewis Freestone, Ben Williams and Tom Bradbury due to injury issues.
After recovering from injury, January arrival Glen Rea made his Cheltenham debut as a substitute on Saturday, and the Luton loanee may be given his first start for the club in midweek.
Liam Sercombe dropped down to the bench at the weekend, but the midfielder is likely to return to the starting lineup on Tuesday.
Derby County possible starting lineup:
Wildsmith; Smith, Forsyth, Cashin, Sibley; Dobbin, Knight, Mendez-Laing; McGoldrick
Cheltenham Town possible starting lineup:
Southwood; Jackson, Raglan, Long; Broom, Rea, Sercombe, Ferry; Perry; May, Keena