The Chelsea star is yet to replicate his club form at the tournament, but has helped Belgium progress from Group H with a 100 per cent record.
Wilmots' men face the Unites States in the last 16 on Tuesday and the former Belgium international has called on Hazard to make the difference as he so often does in the Premier League.
"Eden wants to do more, he can bring us more," said Wilmots.
"Everyone knows that. So now I'm just waiting to see it and I'm not trying to put any pressure on him. I would like him to be a leader on the pitch even if he is just 23."
Wins over Algeria, Russia and South Korea gave Belgium maximum points in the group stage, although Wilmots will likely look for a more polished attacking performance against the US.
Having won each game by a one-goal margin, Wilmots thinks Hazard can be key in helping break teams down.
"He can dictate the game, find the overlaps and score goals," Wilmots added.
"That's what he told me when we talked about it. But between saying and doing there is always a gap. And there is the opponent: will he leave you enough space?
"He was very dangerous against Algeria. I'm counting on him - and so is Belgium - but I think it's all together that we will find the solution."
