Moyes hinted earlier in the week that he was not close to agreeing a new deal to extend his stay at Goodison Park, but Howard has insisted that Moyes is vital to the club continuing their progress on the pitch.
Howard said: "Obviously for us to go forward and have what we have, we need him to be steering the ship. It's vital to keep him.
"I remember talking about this the last time he signed a contract, about how important he is to us.
"The next person who comes in after David Moyes is going to have a very difficult job because the gaffer has done brilliant here."
Moyes has led Everton to fourth place in the Premier League this season.