The Frenchman has netted 10 goals in 16 games in all competitions this season, helping his team to bounce back after a difficult spell last month following a couple of home defeats.
"[Benzema] is the best striker in the world because he does everything," said Mendilibar. "He defends, attacks, helps to play and scores goals.
"There are other forwards who play well and score goals, but this one does everything and if he is on the pitch you have to be alert."
Los Blancos have managed to rediscover their form in the last few games and Mendilibar is adamant that Eibar should be focused throughout the game if they want to get something out of it.
"A month ago it seemed that [Real Madrid] were bad, but in the last five games they have improved a lot and won," Mendilibar explained.
"They are a team that get into the competition when they need to, know how to bring out the competitive streak and win because they have quality.
"When they really compete, it's very difficult to beat them. If we don't come out focused, they'll score two or three against us.
"We have to start the game at full speed, putting the rhythm into it and seeing how long our forces can endure."
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