Gillett branded his relationship with fellow Liverpool co-owner Tom Hicks as "unworkable: and revealed he and his family had been the subject of death threats.
Benitez said: "I have been told about the comments (from George Gillett), but my response is to be really focused on the derby, that is all that I am concerned about.
"But if we win everything will be happier, particularly if it is against Everton."
He added: "Whatever comments are made there is nothing I can do but concentrate on the game and prepare properly.
"I will just be thinking about Everton. I put it out of my mind by working on the games, analysing our opponents and I do not talk too much with anyone. All I want is to have 11 players fit for the game."