The home team are second with three points in the four-team group after they beat Newport County 2-1 on September 3, while the visitors are first with three points after they emerged as 3-1 victors against West Ham United Academy on August 20.
Match preview
Cheltenham were trailing 1-0 after 33 minutes against Newport County, but the Robins took full advantage when Jacob Carney was sent off in the 43rd minute and eventually won 2-1 thanks to two second-half goals from Harrison Sohna and Joel Colwill.
In their most recent match, the hosts lost 2-1 against Barrow on Saturday, a match in which the Robins created no big chances and had just 36% possession.
Manager Michael Flynn said in the aftermath of his side's defeat that he felt his team played excellently in the first half but ultimately ceded too much positional territory and conceded two poor goals.
The result leaves Flynn's side 20th in the 24-team league with 10 points after 10 matches, and they have now conceded 16 goals, the joint fifth most goals per game.
Cheltenham have lost seven of their last 11 games in all competitions, though they have won four of their six most recent competitive home matches.
The visitors come into the clash having thoroughly beaten West Ham United Academy in their first EFL Trophy match of the season, and they only conceded because of an own goal from Harlee Dean in the 38th minute.
Reading had 57% possession, produced 20 shots and only faced five shots themselves, and boss Ruben Selles was thrilled with the performance of his youthful side on the night.
Selles will be less pleased with his team's showing in League One this term given they are 16th in the table with 13 points from nine matches, though they do have a game in hand on eight of the clubs above them and are only three points from sixth-placed Stockport County.
The Royals lost 2-1 last time out on Saturday against Rotherham United, though they did have to play with 10 men after Kelvin Ehibhatiomhan was sent off in the 68th minute when they were trailing 2-1.
Reading have won two of their last three games, but they did lose two of the prior three matches.
The visitors have also been poor away from home this season, losing their last four fixtures on the road and drawing the previous match 1-1 against Birmingham City on August 10.
Cheltenham Town EFL Trophy form:
W
Cheltenham Town form (all competitions):
W
L
D
L
W
L
Reading EFL Trophy form:
W
Reading form (all competitions):
W
L
L
W
W
L
Team News
Flynn may choose to rest Scot Bennett, who has a severely swollen foot, but he is unlikely to be absent for a prolonged period.
Cheltenham will also be without defender Ibrahim Bakare, though midfielder Jordan Thomas and forward Matty Taylor should be fit to start on Tuesday.
Forwards Manni Norkett and George Miller are also in line to start in a front three, with Harrison Sohna and Tom Pett likely to start in midfield.
Reading will be without defender Kelvin Abrefa, who was seen wearing a protective boot after his side's game against Rotherham.
Elsewhere, Selles said that Mamadi Camara, Jeriel Dorsett and Joel Pereira are close to returns but are not ready for Tuesday's game.
Abraham Kanu and Harlee Dean could start as centre-backs in front of goalkeeper Coniah Boyce-Clarke.
In midfield, Charlie Savage may be accompanied by Ben Elliott and Shay Spencer.
Cheltenham Town possible starting lineup:
Day; Kinsella, Laing, Bradbury, Haynes; Thomas, Sohna, Pett; Norkett, Taylor, Miller
Reading possible starting lineup:
Boyce-Clarke; Craig, Dean, Kanu, Garcia; Elliott, Spencer, Savage; Akande, Wareham, Ehibhatiomhan
We say: Cheltenham Town 1-1 Reading (Reading to win on penalties)
Given Reading's worrying record away from home this season, it is difficult to see them taking control of the match against Cheltenham.