Rovers are 9/4 to beat Rotherham United in the Leasing.com Trophy with title partners Sky Bet.
Victory over their local rivals would see Rovers progress to the knock-out stages of the competition after just two games.
When the two teams met in the league, Rovers came from behind to win 2-1. A 2-1 victory for Rovers on Tuesday is priced at 9/1.
Alex Kiwomya is 23/10 to get off the mark in this game, while Alfie May - who got his first goal of the season in Rovers' Leasing.com trophy win over Lincoln City - is 13/5 to get another.
Kwame Thomas could be set to make his Rovers debut on Tuesday evening – Rovers' new striker is 15/2 to get the first goal of the game, or 14/5 to score anytime.