Everton have not won since September 25 and have only scored four goals in the last six games.
Bill Kenwright, Everton's Chairman, visited Benitez at the club's Finch Farm training base earlier this week and Moshiri has also been in regular contact to stress that he has the board's backing.
"I don't want to be here for three years – I want to be here for even more," said Benitez, whose team face a demanding encounter at Brentford. "I want to be here for the new stadium and try to be successful there also. Mr Moshiri, he knows.
"I think Mr Moshiri is quite clever and we cannot complain because he has spent a lot of money. He is someone who is trying to improve the team and improve the club in every sense. He wants to do well but he knows, from when we had conversations in the beginning, they have to support me.
"They have to support the structure in general, so that we can improve. All the conversations with him have been really positive. But we have to be realistic. If we analyse what happened in the summer window and what will happen in January, it's not easy to find exactly what you want."
Benitez also said: "I would say I am talking with the Chairman at least three times a week. I'm talking with Denise (Barrett-Baxendale), with Marcel (Brands); I'm talking with Mr Moshiri, so I am in contact all the time with the people on the board and the people who really care about the club."
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