The band - which also consists of Dappy and Fazer - allegedly argued while on their way to a show in the North of England after Contostavlos revealed plans to crack the US solo.
"It all got completely out of hand on the bus on Friday night," a source told The Sun.
"They were on their way to a gig up North when Tulisa told the band how she was getting close to fellow X Factor judge Kelly Rowland and how they had discussed her cracking America."
The insider added: "She also went back on a deal with Dappy and Fazer to use X Factor to break the band worldwide.
"Instead of N-Dubz performing on the show, Tulisa is planning to use a key slot on the show to promote her solo career. She has even talked about a collaboration with Kelly."
The decision is said to have angered Dappy and Fazer as they saw Tulisa's role on The X Factor as "a launch pad" to promote the band "as writers and producers".
The report follows the announcement that N-Dubz have parted ways with their US record label Def Jam due to creative differences.
Meanwhile, Dappy is preparing to release his debut solo single 'No Regrets' on September 18.
> N-Dubz Dappy: 'The X Factor gives unfair fame'
Watch the music video for Dappy's new single 'No Regrets' below: