On Friday Benitez hit out at United counterpart Sir Alex Ferguson, who he claimed was allowed to go unpunished when criticising referees.
Gill is a leading member of the FA board.
“They were saying we are not a threat,” said Benitez in the Daily Mirror. “Now they know we are, they are starting mind games.
“But I don’t think it’s a mind game when you have control over everything, it’s a mind game when you have the same level as the other people, then you can show you are cleverer than the others.
“But when you have control of everything and your chief executive is powerful in the FA and things like this, then that is not mind games.
“Is there a conflict of interest with David Gill at the FA?
“That is another fact. It is a fact that one person has a lot of power and control, and is on a lot of committees in the FA.
“To me that is very strange.”
