The 28-year-old striker heads to Anfield with the Black Cats on Saturday having struck three goals in two games and formed a potentially crucial partnership with fellow forward Jermain Defoe.
Moyes reunited with Anichebe – whom he had described as “a young Didier Drogba” during his Everton days – this summer after the Nigeria international was released by West Brom.
Moyes warned: “We’ve just got to be careful – we’ve won two games with Victor coming into the team and we also played well at Southampton and should still be in the cup.
“But let’s put it into context – he’s not a £20million centre-forward. We’ve got a centre-forward who I believe in and I know what he is capable of but there will be games when he is on top form and games when he is not.
“We’ve been really pleased with him and Jermain – what Jermain has done whether it be this season or in seasons gone by speaks for itself with his goals.”