The Uruguayan has made headlines on the pitch rather than off it since returning from a 10-game ban for biting Chelsea's Branislav Ivanovic last season.
Suarez has netted three goals in as many games and struck up a formidable partnership with Daniel Sturridge.
Liverpool headed into the international break behind Barclays Premier League leaders Arsenal only on goal difference, and Suarez's desire for excellence is just what Rodgers wants to see.
The Reds boss told liverpoolfc.com: "With Luis, he demands the best from himself and his team-mates at all times, and we saw that against Crystal Palace, even right at the end when the game was won.
"You see his work-rate and his demand for a better ball into the box, and that's what we want.
"There was a moment in the first half where he chased back on the left and won the ball, too. There is no doubting his commitment and there is no doubting he will always have that desire at all times.
"That attitude from Luis to demand the best is exactly what we want. We can't accept just winning and say it's all right."