The 23 year old has been described as the world's third-best player after scoring eight goals in his last six games.
"He's enjoying it at Spurs. I wouldn't see him in any rush to leave," King told BBC Sport.
The Wales international has been linked with a big-money switch to Spanish champions Real Madrid because of the quality of his recent performances.
"Gareth is in the top three players in the world on current form," he said. "I really enjoyed playing with him. Last season was his best to date and now he is taking it to another level."