The running back has spent the last three seasons with the NFC North side, but is due to become a restricted free agent later this year.
The 27-year-old told the team's website: "I do understand I'm a restricted free agent and I understand how the business works and I would like to just bypass all of this and sign a long-term deal.
"Just knock it out. I don't want to go anywhere. I know the fans don't want me going anywhere. I know the team doesn't want me going anywhere. The front office doesn't want me to go anywhere, so let's just make this happen.
"I love this franchise. I grew up watching it. I worked here. I always dreamed of playing here, so let's make the best of it."
Bell, who split the rushing workload with Reggie Bush in 2013, finished the season with 650 rushing yards, 547 receiving yards and eight touchdowns.