The 31-year-old has been plagued by knee problems in recent years and had more surgery at the end of the season.
"I've been discussing things with the club," King told the Spurs website. "The club has been fantastic in supporting me and given me several options to stay involved.
"I shall take a view with them in pre-season on my future. Tottenham has been the only club for me and if I can't play here then I shall look to be involved in another capacity."
Other Premier League players out of contract include Arsenal goalkeeper Manuel Almunia, Andy Johnson and Danny Murphy of Fulham, Aston Villa's Carlos Cuellar and Emile Heskey, Liverpool's Fabio Aurelio, Manchester United keeper Tomasz Kuszczak, Stoke City's Ricardo Fuller, West Bromwich Albion's Paul Scharner and Hugo Rodallega of Wigan Athletic.
Chelsea's Champions League winners Jose Bosingwa and Salomon Kalou were also on the league's free-transfer list.
Defender Bosingwa, signed from Porto in 2008, and forward Kalou, who spent six years at Chelsea after joining from Feyenoord, follow Didier Drogba out of Stamford Bridge.
Drogba, who scored the decisive penalty in the shootout victory in the final against Bayern Munich last month, announced last week he was leaving after eight years with Chelsea during which he also won three league titles, four FA Cups and two League Cups.
The 34-year-old has been linked with Real Madrid and Chinese club Shanghai Shenhua.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.