The couple - Whitney Houston's biological daughter and adopted son - announced their betrothal in a trailer for reality show The Houstons: On Our Own last month.
However, Gordon has now clarified on his Twitter page that the couple are not involved romantically.
"@REALbkBrown and I are not engaged or dating," he wrote. "Just close like we have always been."
Meanwhile, a source confirmed the split to Us Weekly, saying: "It will come out in the show."
"I think it has to do a lot with the family not liking Nick, considering he was a godson and then they became a couple," another insider said. "I'm sure there is a lot of 'Would Whitney be okay with this?' going around."
The Houstons: On Our Own airs on Lifetime.