Mourinho has come under fire following United' poor start to the campaign. The Reds are six points adrift of leaders Manchester City after eight games.
However, Essien, who knows Mourinho as well as anyone having worked with him at Chelsea and Real Madrid, is confident that his former boss will come out of the current situation smelling of roses.
"As a player, he had a very big influence on me. He was the one who brought me to Chelsea and he took me with him to Madrid to play under him," said Essien.
"There is such a great relationship between us. He is just a great manager and I know that he has been having a bit of a tough time in Manchester, but knowing him I think he is going to turn it around.
"I am backing him because I am still going to be his No.1 fan!
"I have to back him to turn things around and it is a difficult situation but I am sure that he can do it.
"You know that when you play under Mourinho, you know you are going to win titles. He has been at United for two or three years now and he has been winning trophies.
"This season seems a bit difficult now but the season is still long and they still have a lot of competitions to play."