Clarke is expected to be without injured trio Will Puddy, Mark McChrystal and Lee Mansell, though, as Rovers look to bounce back from a home defeat against Northampton on Saturday.
“I am not into prioritising between the league and the cup, I simply want the players to try and win every game,” Clarke told www.bristolpost.co.uk.
“We want to finish as high up in the league as we can, but we also want to get as far as we can in all of the cup competitions. That is the mentality I want my players to have.”
Birmingham boss Gary Rowett is expected to make changes for the trip.
Blues beat Reading 2-1 in their Sky Bet Championship opener on Saturday but Rowett will shuffle his squad at the Memorial Stadium.
The 2011 winners were knocked out in the second round by Sunderland last season and Rowett wants to ensure he strikes a balance in the league and cup.
He said: “In an ideal world you want to advance but you always get that debate in the competitions when you have a small squad and you are trading it off when you get three or four injuries and suffering in the league. There’s always that balance of giving one or two players a breather and some an opportunity.”