Should the Reds – who lost 1-0 at home to Luton Town in their first Championship game of the season on Saturday – win at the Riverside Stadium in the 6pm kick-off, they will visit Premier League giants Chelsea in the next round.
Struber said: "My focus is on Middlesbrough and our performance and making the next step in our style. After that we can speak about what is the benefit and if we have Chelsea in the next round. It is very helpful to have another game now to make the next steps.
"When we see the transfer value of Middlesbrough and our value, we know we have a very big job. It is a team with very high individual qualities, especially (Britt) Assombalonga and (Ashley) Fletcher up front. They are very quick and very physical. It's a good chance for us when we stay together with good discipline. It won't be easy for Middlesbrough.
"I know the experience from their coach (Neil Warnock) is very big and he has a clear plan for his players. It is difficult for us to beat them but it is possible. I trust my boys to change their style from Saturday, we must do this to win this game.
"We will look to change some players. Many players had a big workload and we will give other players the chance to play. I trust my whole squad. It is a big chance for players to fight for a place in the first 11."
Left-backs Clarke Oduor and Ben Williams will miss the game while Callum Styles is a doubt after picking up a knock in the game against Luton on Saturday. Aapo Halme could feature after missing the last match due to a facial injury.
Struber said: "Callum took a hit in the game and we will see him in training. I hope he is ready. Aapo is OK now. He is back."
Struber was disappointed with the performance of his players on Saturday. He said: "The only thing we can do is put the Luton game behind us. We know it is not the performance we expected. We learned from Saturday and we can show that tomorrow. Middlesbrough have maybe a similar style with many long balls and a lot of fights for the ball. The boys can show me a better performance.
"At the end of last season we played very well against long balls and we did well against Luton in many situations. It is more a problem when we are on the ball. We need to play quick and with a good style.
"It needs a massive step in energy from the game against Luton. We need more bravery and a clear plan in possession to break the lines. I hope everyone is ready for a big fight."
Barnsley are looking for new players. Struber said: "We get closer and closer. We look in many positions. It is a big challenge to find the right players and the player who can help us with the right quality. We have no stress, we work with a good focus and we will find the right player. We need the necessary time for that.
"The Luton game showed me we need players who have a physical advantage. I hope we can find that and we are very close with one or two players. I hope we can sign them in the next days or the next weeks.
"I am hopeful. It is not always in my hands, I need my owners to give a big impact to handle the situation with the new players. But in the end I hope we have a good signal from the owners and we can find the right players."
Asked if the arrivals would have experience in the Championship, Struber said: "I think they have the quality to play in the Championship. This is the most important thing."