So far highly-regarded Moyes, 49, has refused to commit beyond that date - and Everton keeper Howard believes that is a genuine cause for concern.
Howard, 33, said: "It's a difficult conversation to start talking about where we go if the manager leaves. But it's a conversation I want to have. It's important.
"He's obviously the figurehead of this club. He's become the person everyone looks to.
"Whether a board member, a fan, a player, or a casual observer, your focal point is David Moyes.
"Everything trickles down from there. We have to have him in place."