The 38-year-old goalkeeper is into his ninth season with the Saints, and he does not see himself leaving the South Coast club when his current deal expires in the summer of 2016.
"I would like to continue supporting the club in some way," he is quoted as saying by the Daily Echo. "It would be very easy for me to sit here and go 'I'd love to be a coach at the club' and that probably would be a natural progression.
"I'm still to do the qualifications, and that is something I'm looking into now, and then from there we'll see. Things can change, but I think that, in a perfect world, I would be doing some kind of role within the club.
"If I feel like I do now at the end of this contract, then I'd expect to continue as a pro and continue doing what I'm doing in the dressing room."
Davis has made 293 appearances for the club.