A source told Britain's Daily Mirror newspaper: "Brody thinks Nicole is
vulnerable. He wants to move in and cook for her."
Meanwhile, Nicole has slammed rumours that she was admitted to a rehab
clinic to help her get over an eating disorder last week.
The star - the adopted daughter of singer Lionel Richie - posted a personal
message on her MySpace page refuting the claims.
She wrote: "I did not check myself into an eating disorder rehab. I don't
know why or how this rumour started, but I am home, in Los Angeles, and very
happy.
"I do not have an eating disorder, and I don't know how many times I have to
say it."

Meanwhile, Nicole's dad , Lionel Ritchie says his daughter's weight is making him miserable.
The 'Hello' singer admits he constantly worries about his super-skinny daughter and wishes he could help her to be happy.
He told The Knowledge magazine: "She is going to be OK, she is going to be OK. She recently broke up with her fiancé and she is a worrier like her father. It worries me that she worries.
"You're only as happy as your saddest child. I look at the adult she has become and I just want to scoop her up."
Lionel, who missed fifteen consecutive Christmases at the height of his career, reveals Nicole had an unusual childhood and was surrounded by famous neighbours.
He explained: "We would be driving along and I would say to Nicole, 'That's Uncle Prince and that's Uncle Michael (Jackson) and there's godfather Quincy Jones.'"