Garnett has played for 19 seasons in the NBA, with the 38 year-old spending the majority of his career with the Minnesota Timberwolves.
King revealed to ESPN on Wednesday that the Nets believe that Garnett is still under contract and will play next season, barring a change of heart from the player.
Asked if Garnett can continue to play at a high level, King said: "Yes. I think he's preparing earlier this year than he did last summer in order to prove that he can."
The veteran averaged 20.5 minutes a game last season, scoring 6.5 points and 6.6 rebounds for Jason Kidd's team.