Rodgers has staunchly backed his star striker since taking over from predecessor Kenny Dalglish, who did exactly the same last season. And while he accepts the player has been - and most probably will always be - dogged by controversy that is not the full picture.
Rodgers said: "He is not malicious, it is just his nature. He is a sensitive boy as well and he seems to cope remarkably well with everything. He will always be a topic for conversation but that's because he's a top player."
The Reds boss had cause to speak to the Uruguay international on Thursday to reprimand him over an admission he dived in an attempt to win a penalty earlier this season.
That confession, in which the 25-year-old said "I was accused of falling inside the box in a match, and it's true I did it that time", brought words of censure from Rodgers.
"It is unacceptable. It is not something we advocate here. Our ethics are correct," he said. "I've spoken to Luis and it will be dealt with internally."
He added: "He has been a topic for people, particular for the media, because of his great moments of football and things which have happened off the pitch.
"The majority of this season has been based around his performances on the field, in which he has shown the true top player he is.
"In fairness to Luis he has knocked on my door and actually apologised as well. He got booked in a game (against Southampton) where he instinctively handled the ball and the very next day he came in and apologised for it.
"It is instinctive with him, that is the type of player he is."