In Saturday's third round, the native Austrian shot 5-under-par 66, and is 15-under 198 overall.
"It's always been my goal to win my first European Tour event here at Fontana in front of my family and friends and I think if I can do it would be the best day of my life after the birth of my kids and my wedding day," said Brier, who set a tone on Thursday with a hole-in-one. "It's everything I have worked for and to do it here would gorgeous."
England's Simon Dyson (67), who was the leader briefly on Saturday, is one-stroke back alone in second place at 14-under 199.
Both players shot 2-under 69 and are 9-under 204.