The label is said to be keen to have the star – who is often spotted sporting the brand's trainers – on board, but she is reluctant.
"It's no secret how much Kristen loves Nikes. She often changes into a pair of Nikes after walking the red carpet in heels," a source close to Kristen told RadarOnline.
"It's not the easiest deal to make, as Kristen has shunned dozens of offers to endorse products since her rise to fame in the Twilight films.
"Also, Kristen already makes a ton of money because she gets a little piece of the Twilight merchandise. She's terribly self-conscious about seeing her face on products."
Nike have had collaborations with several high profile faces including Michael Jordan and Lance Armstrong.
"But the company obviously wants to broaden its base from athletes to actors, and, in particular, appeal to young women," the source added.
"Nike execs believes that with her tomboy cool image, Kristen would be the perfect celebrity spokeswoman to create some excitement about the brand."
If Kristen does decide to cut a deal with Nike, it's going to cost them.
"Nike will have to roll out some serious money if they're going to be able to close a deal with her," they said.
Kristen has been extremely selective about fronting campaigns since shooting to fame. She has been the face of Balenciaga and is currently the face of the fashion house's perfume Rosabotanica.
In December, she was revealed as the new face of Chanel. Her campaign with the French label will be shot by creative director Karl Lagerfeld himself and will be released sometime in 2014.