Wigan boss Roberto Martinez is the favourite to take over, while Brighton manager Gus Poyet and Celtic's Neil Lennon have also been linked.
Howard told the Liverpool Post: "We are a really strong group of quality players and the foundations are set.
"The table is set for the next guy and I have no doubt, if he is a strong character, a guy who can lead us well, we will have no problems.
"It's just very rare to replace one long-serving manager with another long-serving one so we will need to fill the vacancy with a very strong character. And I have no doubt that will happen."