With Albion in search of a successor to the sacked Pepe Mel, the 42-year-old was being hotly tipped to move to The Hawthorns despite his lack of managerial experience.
Clement himself initially stated "the time for me to be a number one is soon", thanking Ancelotti for providing him with the belief he can make the step up after working alongside the Italian at not just Real, but also Paris St Germain and Chelsea.
But Clement, whose brother Neil played for Albion for 10 years from 2000 to 2010, has now suggested his time with Real is far from over.
"Working for Real Madrid is a fantastic experience and I'm very happy here at the moment," said Clement on 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."
When it was suggested to Clement a potential move may come sooner rather than later, he replied: "Possibly, but we'll just have to wait and see.
"I'm working at a fantastic club every day, we've 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 La Liga title, Copa del Rey and Champions League.
"It's exciting times for Real Madrid."
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