While in attendance at this week's WWE SummerSlam Party, Lutz told reporters that he was thinking of joining forces with Pattinson to create a new collection.
"Rob and I were talking about doing a clothing line together!" Lutz said.
The Immortals star already has his own line called The Abbot + Main.
"[Pattinson] didn't know I was doing mine," Lutz continued. "He's like, 'I should do one' and I'm like, 'Oh'. And he found out I was doing one and he's like, 'Really?' It was really funny. He wants to do one too."
The actor then went on to suggest some names for a potential collaboration.
"What'd we call it, we called it 'Rags by Rob' or something, because he's always so like, I don't know... hipster."
Pattinson recently shared his take on the sex scene in The Twilight Saga: Breaking Dawn - Part 1, revealing that he wanted Edward to cry after consummating his relationship with Bella (Kristen Stewart).
In July, the 25-year-old described the film's birth scene as "hardcore", insisting that the scene in question will be gory.
Watch the teaser trailer for The Twilight Saga: Breaking Dawn - Part 1 below: