The 33-year-old retired in 2012 after a series of knee injuries prevented him from playing more than a bit-part role for Spurs, for whom he made 323 appearances.
King is currently an ambassador for the North London club, but he has said that managing Spurs remains an ambition of his.
He told BBC Sport: "I will complete my badges and it would be a dream come true for me to lead the team out as a manager.
"It is early days for me still. I've got a lot to learn on that side and I realise how difficult it is.
"I will take my time, try to get my badges and all you can do is see where you go from there."
King also made 21 appearances for England.