The Welshman spent the season away from Manchester City, scoring 11 goals in 35 appearances for the Bluebirds, and according to Jenkins he is keen to stay on next season.
Some reports have linked Bellamy with the vacant managers role at Cardiff but Jenkins dismissed that notion, saying the club is unlikely to have a player/coach.
"Craig has indicated he will like to play again for Cardiff next season and if that happens it will be fantastic," he said.
"We have had an initial conversation with his agent and said we remain open to offers.
"We will sit down and have a chat with Manchester City and his agent once we have a manager in place.
"I don't think it is likely at the minute (that Bellamy could become a Cardiff player/coach). We'd love to have Craig back as a player but we'll see what happens."