Spurs still have hopes of winning the Premier League title this season, and they are currently lodged just seven points behind league leaders Leicester City.
The Lilywhites’ next challenge will be to ensure that they continue to compete for the title in the years ahead.
And King feels that the squad is already in place to enable them to do that, with only a supplementary striker required in the summer transfer window.
“It’s a really good time to be a Spurs fan right now. You always look to strengthen with quality additions,” he said, when asked which player Spurs need to move to the next level.
“Perhaps someone else could come in and ease the goals burden on Kane. But it’s a strong group already.”
Tottenham have the youngest squad in England’s top flight so, in theory, they should only become stronger as they become more experienced.
Mauricio Pochettino has built a squad packed with talent, and he is yet to spend too lavishly during his time at White Hart Lane.
Tottenham have been linked with a series of players ahead of the summer transfer window, but whether Pochettino wants to disrupt the balance of his current squad remains to be seen.
Spurs have five games remaining if they want to catch Leicester at the top of the table, with their next match coming against Stoke City at the Britannia Stadium on Monday evening.