The 19-year-old left-back joined Carlisle at the start of the season, but sustained a hamstring injury in his second appearance for the club in the Capital One Cup penalty shootout win over Blackburn in August.
"Reece is a great lad and has been absolutely first-class since the moment he came up here," caretaker-manager Graham Kavanagh told the club's official website.
"He settled quickly, he was getting games and he was just really unfortunate with the timing of his injury.
"We brought Conor Townsend in from Hull as cover and we are now in a situation where Chris Chantler is well ahead in terms of where we expected him to be with his recovery."
Chantler has yet to appear for Carlisle this season following two ankle operations, but has stepped up his recovery and is currently training with the youth-team squad.