The Belgian stated on Thursday that he might have to move to Spain to win the coveted prize, where it has gone for the past decade.
"He can do it, this guy is talented enough to do it - he has the ability, he has everything," Schwarzer said on Sky Sports' The Debate when asked what has held Hazard back.
"It's all in his head.
"I've seen a difference in him since I was at the club.
"When I was there, I said after a game where he was phenomenal, 'You'll have to do that every week and you can do that every week'.
"His response to me was 'some weeks I play well and some weeks I don't'."