Pepe Mel lost his job at The Hawthorns at the end of the season despite keeping the club in the Premier League, and Clement's name had been touted as a possible replacement for the Spaniard.
The 42-year-old is currently Carlo Ancelotti's right-hand man at the Bernabeu having previously worked with him at Chelsea and Paris Saint-Germain.
Though Clement has expressed his desire to become a head coach in the future, he is fully focused on helping the newly crowned UEFA Champions League winners lift more trophies next season.
"Working for Real Madrid is a fantastic experience and I'm very happy here at the moment," he told talkSPORT. "My family are settled and we'd like to stay and enjoy this experience.
"I do have ambitions to make that step up to management at some point in the near future, and if the right club comes along at the right time then I'd like to do it.
"But at the moment I'm just going to enjoy my time here.
"I'm working at a fantastic club every day, we have great players here and we're competing for big trophies.
"Next year we'll play in the game against the Europa League winners (the UEFA Super Cup); we'll be in the World Club Championship as well as competing for the Liga title, Copa del Rey and Champions League.
"It's exciting times for Real Madrid.''
