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.
