The Everton manager heaped praise upon American Howard ahead of his 200th consecutive Premier League game - a landmark that puts him second to Tottenham's former USA international Brad Friedel, who is still some way ahead of his compatriot with 310 consecutive appearances in the top flight.
However, although Howard still has over three years remaining on his contract, Moyes told reporters that the search is on to find the shot-stopper's successor.
“You are always planning for who is the next Nigel Martyn, who is the next Tim Howard," he said.
“We are always looking to see who that next one would be. You have to do that.
“We have asked a couple of times about [Birmingham and England keeper Jack] Butland, but not recently.
“We are just looking out. Chris Woods [Everton's goalkeeping coach] is a big part of Tim because he works for the US national team as well, now.
“But Chris also does a lot of work looking at the future goalkeepers for us. It is a bit of a specialist job.
“We can all look at goalkeepers and say ‘he comes and catches it’ or ‘he makes good saves, he has good distribution.’
“But to understand the technique in goalkeeping is a bit more specialist really.”