Essien signed for Real last month on-loan from Chelsea.
"Having monitored the off-season games that Michael has featured in for Chelsea I can certainly see him getting back to his best this year, but we will have to wait and see whether that happens when he features for Real Madrid," Appiah said.
"Obviously, a lot can happen in football, but we hope that Michael can stay fit and get back to the level that we all know he is capable of.
"The chance to work with Mourinho again might help because Michael played some of his best football under him at Chelsea.
"However, his lack of football in recent years has given other great players, such as Prince Buaben and Emmanuel Frimpong, the chance to shine and if he isn't around they are more than good enough to fill the void."