Koeman reportedly finds himself under pressure at Everton with the club registering just two wins from 11 games in all competitions, and Moshiri was seen at the club's training facilities last week.
However, Koeman has revealed that Moshiri was on the premises to look at a recent development, and the Dutchman said that he maintains the full support of the club's hierarchy.
The 54-year-old told reporters: "Yes he was here with Bill Kenwright and more people from the board because they hadn't seen the new building. You speak about football of course.
"There wasn't really a message. They are behind the team and the manager. In football that's a nice thing but in football it's all about results. Until now it's total support from the board, yes."
Everton are next in action when they host Lyon in the Europa League on Thursday night.