The Frenchman will join Real after the Euros.
Anelka told Marca: "Mbappé has two or even three players on him every time he has the ball, so it is difficult to make a difference in these conditions and on top of that he has had a nose injury, but he is a fearsome player who can score at any moment and he's going to show it soon. You'll see!
"I think he has had a good season... he has good statistics but people always want more."
He added: "I don't think it will be difficult for him to adapt to Real because there are French players of his generation who will help him."
Anelka also said of Real midfielder Arda Guler: "Turkey is also doing very well, with a young team and a very good coach. Everyone is watching out for Arda, who is showing all his talent despite his young age. He is going to be a great player for Real Madrid and for Türkiye."