The 30-year-old, who had never played top flight football before this season, has impressed in Leicester's opening three games of the campaign.
Moore believes that he and Morgan will improve their partnership in the centre of defence as the season progresses.
"Wes has been exactly the same this season as the last two seasons – outstanding," Moore told the Leicester Mercury.
"It is a shame for him that it has taken him this long to get to this level, but he is doing everything he can to prove he can play at this level and, hopefully, he will finish his career in the Premier League in five or six years' time.
"It has been a big test so far but, as a partnership with Wes, I feel we are growing and, as the season goes on, we will find ways to nullify these teams and keep more clean sheets."
Morgan joined Leicester from East Midlands rivals Nottingham Forest in 2012.