The 34-year-old, who has recently returned from a fractured skull, is out of contract in the summer but talks are underway regarding a new deal.
"I want to stay and end my career with the club," Carey told the club`s official website.
"With no disrespect to anyone else or other clubs, I don`t want to be dropping down the divisions to keep playing.
"I`d like to end everything with my hometown club at a decent level."
Carey has made 603 appearances for City, the second highest in the club`s history behind John Atyeo.
Source: PA
Source: PA