Victory over the Robins saw the West Yorkshire side climb into fourth in the Championship after three successive defeats. Samuel Saiz scored twice before Pierre-Michl Lasogga made it three in the second half to secure the three points at Ashton Gate.
Christiansen's side face a run of three games in seven days starting with the trip to the King Power Stadium, with Leeds hosting Sheffield United on Friday (27 October) before facing Derby County at Elland Road the following week.
But despite the rigorous upcoming schedule, Christiansen has hinted he will retain many of the players who delivered the weekend win.
"I am looking at both games (Sheffield United too)," he told the media, according to the Yorkshire Evening Post. "And I am looking at the players in the squad that I have. Leicester had a good win this weekend, a win that can give them good confidence back. I think both the league and the cup are important.
"I don't have to tell them when they play and when they don't. If the players want to speak my door is always open. At the moment we have a game tomorrow and the first XI have an opportunity to jump in. It's a beautiful opportunity for them."
A family bereavement means winger Stuart Dallas is missing for a second game in a row, while Gaetano Berardi is suspended following his red card against Bristol City. Cameron Borthwick-Jackson is set to continue his run of playing in every round of the Carabao Cup, but Caleb Ekuban remains out with a broken foot which has forced him to miss the last 11 games.
Having knocked out Sean Dyche's Burnley in the last round – following wins over Port Vale and Newport County – Leeds have high hopes of causing another cup upset against managerless Leicester. Caretaker boss Michael Appleton guided the Foxes to their first win since the sacking of Craig Shakespeare, with a 2-1 win at Swansea City on Saturday (20 October).
Leeds have not played at Wembley since losing the 2008 League One play-off final to Doncaster and Christiansen is aiming for a return 10 years on.
"[Wembley] That's a big word," he added. "I will try to win all of the games and try to pass through as many rounds as possible. If we win progress in this cup we will try to do it but we have to face the reality that we have faced one Premier League team and we are going to face another one. It's difficult but we have to enjoy the moment. We can dream."