Parker has been imperious for West Ham this season.
"It depends what the captain is. Fifteen years ago the captain shouted at the players, today they lead by example," Grant said. "Always, with everything, Parker does this. When I want to check players I do it when there are difficult times because when things are good everybody is a genius. And he is good in a difficult time."
But Grant rejected the suggestion that he would like to make Parker his captain, saying: "No, we have a captain now. I think Matty (Upson) is doing well. Parker is a second captain."