Anichebe burst onto the scene at Everton in 2006, scoring his first Toffees goal against the Baggies in his third game, and knows the scrutiny young stars come under.
He said: "I told him about that. I came through with James Vaughan, who was a big deal, as it always is when a young guy comes through.
"It is very difficult and you can get caught up in the hype but as long as you have good people around you then you should be okay.
"As much as they're building him up now, if he starts playing badly people will bring him down again.
"As soon as you don't have the level of performances you should have you will find it difficult, but he's a good kid and is positive and really believes in himself so I'm sure he'll continue to fulfil his potential.
"I always sing his praises because he's a quality player and he will be a quality player for years to come if he can keep his head right.
"He is young and there is a lot of pressure and expectation on him right now, but as long as he can keep doing exactly what he's been doing, not listen too much to the media and things on the outside and keep his feet on the ground, he will be fine."
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