The Tottenham defender, who has constant injury issues to deal with, is not on the retained list provided by the club to the Premier League but he has not ruled out signing a new contract.
King has no appetite to join another club however and if he cannot continue playing will stay at Spurs in a non-playing capacity.
He told the club's official website: "I had a really good start to last season and was pleased to play as many games as I did.
"A knock in training set me back towards the end, but I opted to carry on playing rather than take the time out to have the knee seen to.
"Unfortunately that meant that I didn't play the last few games at the standard I would have liked.
"I've been discussing things with the club and my contract expires this summer.
"The club has been fantastic in supporting me and given me several options to stay involved with Tottenham. I shall take a view with them pre-season on my future.
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"Tottenham have been the only club for me and if I can't play here then I shall look to be involved in another capacity."
All clubs are required to submit their players released and players retained lists to the Premier League by the third Saturday in May, apart from Chelsea who had a deadline of four days following the Champions League final.
Some clubs have since offered new deals to some players - for example Paul Scholes at Manchester United.
Other notable players not on their club's retained list include Arsenal goalkeeper Manuel Almunia, Owen Hargreaves at Manchester City and United's Michael Owen.
Press Association Sport understands that Fulham are still in talks with Danny Murphy and Pavel Pogrebnyak about extended stays, but Andrew Johnson is set to leave Craven Cottage this summer.
The Cottagers are hopeful of extending the contracts of captain Murphy and Russia international Pogrebnyak in the coming weeks, with discussions ongoing and offers made.
However, it is understood that Fulham are not in discussions with striker Johnson, midfielder Bjorn Helge Riise or defender Zdenek Grygera about new deals.
Emile Heskey and Carlos Cuellar are both on Aston Villa's free transfer list, as is Fabio Aurelio at Liverpool.
United keeper Tomasz Kuszczak is not on the retained list, and Danny Guthrie, Peter Lovenkrands and Alan Smith are all on Newcastle's free transfer list.
Wigan have a number of players on their free transfer list that could interest other clubs including striker Hugo Rodallega and midfielder Mohamed Diame.