Anichebe has failed to establish himself at Goodison Park since making his debut in 2005, but after scoring eight goals in 26 appearances this season, Moyes has admitted that the 24-year-old could become an "outstanding player".
The 49-year-old reporters: "He has been terrific. The boy has an awful lot going for him and I've said many times he's just needed to have a bit more self-confidence.
"I think he has a bit more to do but we have got signs of someone who could be an outstanding player."
The Nigerian international is likely to feature when Everton play Arsenal on Tuesday evening.