The 33-year-old, who moved to the Etihad Stadium from Atletico Madrid last year, will come to the end of his current contract at the end of the season.
Demichelis will face competition from new £32m signing Eliaquim Mangala, but the Argentine is hopeful that he can stay with the Premier League champions for another year.
"I am playing every game, every two to three days, so I am just enjoying it and taking it game by game," the Manchester Evening News quotes Demichelis as saying.
"I would be happy to stay this year and then one more year because I think I will still have the quality to play at this level."
Demichelis scored a late equaliser in City's 2-2 draw with Arsenal at the Emirates Stadium on Saturday.