Beevers told the Lincolnshire Echo: "We've opened talks with the club and it's ongoing at the moment. I'm just leaving it to my agent and the club to sort something out.
"I'm happy to stay. Everyone knows I like it at Lincoln and I feel I'm playing well at the minute. I'm very happy with things."
Beevers is one of three players to have been offered a new deal at Sincil Bank, along with Adrian Patulea and Dany N'Guessan.
Manager Peter Jackson said: "We're just waiting for them to get back to us. Hopefully there will be more news this week."