The 29-year-old, who is one of the highest paid players at Kenilworth Road, will see his current deal expire in the summer.
And even though the Hatters are expected to cut costs, Davis is desperate to help them back into League Two.
"My contract finishes in the summer. I would like to stay. I would like to help Luton back into the Football League," Davis told the Herald and Post.
"The club and the fans have been brilliant to me since I've been here. I would like to repay them.
"Whether I stay or I go I have to take a pay cut. I want to be a part of Luton Town. I look at Luton as my home now. I want to help get the club back up."
Meanwhile Hatters captain Kevin Nicholls will miss the start of next season after the FA upheld their decision to hand him a five-match ban.