The Nigeria international made his Toffees debut in 2006 and had been tipped for a big future.
However, while injuries and inconsistent form have restricted the 23-year-old's appearances in recent seasons, Moyes has suggested that it's time for the player to fulfil his potential.
"Victor has great potential," Moyes told the club's official website after seeing Anichebe find the net during Everton's 3-1 victory over DC United.
"Probably a lot of people seeing him for the first time [in America] would say 'wow, he's a really good player'.
"He has had a few injuries and if he can get rid of them he has got things you can't buy - great strength, great pace and power, and he took his goal really well."
The centre forward has made nine appearances for Nigeria, scoring one goal.