Moyes is in the final year of his contract at Goodison Park and he revealed earlier this week he was in no rush to sign a new deal.
Howard believes keeping Moyes is central to Everton's future plans and admits whoever does finally replace him faces a tough job, likening it to Manchester United's search for a successor to Alex Ferguson.
"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," said Howard.
"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.
"When you have longevity and success, it's hard to match. It's a very similar situation here at Everton to United and after Ferguson."