The former Chelsea midfielder faces Vidic in the Milan derby on Sunday, in an echo of their tussles in the Premier League.
Essien said: "I think he (Vidic) is being missed by United because things are not really going well for them, especially when it comes to their defence.
"He is a top guy and really good defender. He gives everything and puts his body down for every tackle. It will be good to face him in another league. I will be looking forward to it and hopefully we will win."
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