Goodman, 21, signed a professional contract with the Lions in the summer of 2012. Capable of playing right-back or in central defence, he was named as a substitute on three occasions during the 2012/13 campaign.
During the latter stages of that season he enjoyed a successful spell on loan at then Conference club Luton Town and was rewarded for his continued progress when he signed a new one-year contract at the New Den. He joined Aldershot Town on a youth loan at the start of the 2013/14 campaign to gain more valuable match experience.
Meanwhile, attacking midfielder Harry Williams has been recalled from his loan spell at Evesham United and will feature at the Filton Academy Ground and left-back James Bowen, who made his first team debut at Stevenage on Saturday, is also included.
Cheltenham and City are in a group with Newport County, Plymouth Argyle and Portsmouth in the competition. Cheltenham's opening game resulted in a 3-1 home defeat by Pompey, for whom Ryan Taylor scored twice, with Conor Chaplin also on target. The Robins' reply came from Zack Kotwica.
Cheltenham Town Reserves (from): M Gould, J Hanks, J Deaman, J Goodman, J Bowen, A Powell, O Sterling-James, A Haworth, Z Kotwica, B Dale, H Williams, H Reynolds, D Reynolds, R Daly, A Dinsmore, C Craddock.