The duo, who are currently filming the movie 'Fury' in Oxfordshire, England, have always wanted to work together but allegedly aren't getting along well on set between scenes because they are so different.
A source told gossip website RadarOnline.com: "Brad likes to enjoy himself on a set, but Shia is an incredibly serious guy when it comes to his performances.
"They have very different styles of working and it's not mixing well on a personal level, which is tough because Brad and Shia met many years ago and wanted to work together. They searched a long time until they found the right project and both were enthusiastic about the World War II army thriller."
The source insisted that Brad, 49, is still very impressed by his 27-year-old co-star's acting talents.
The insider said: "Brad is impressed by the performance Shia is turning in, but it's not helping their friendship for Brad to see how much torture Shia puts himself through to get results.
"Brad is a laid back guy who works completely differently from this kid."
Brad likes working with younger actors and was hoping to form a close bond with Shia, similar to the one he developed with Jonah Hill on 'Moneyball' in 2010.
The source said: "Brad loves to joke around with his young co-stars. And especially on a very serious war movie, he'd love to take the edge off by kicking back between scenes. But Shia wants to stay in character the whole time."