The Uruguayan international made the claims in an interview with Fox Sports Argentina, saying he went down in the box in the match against Stoke in October with the view of conning the referee.
Suarez has for long come under fire for his antics, with Rodgers always defending his player, but the latest admission has left the Northern Irishman fuming.
“It's unacceptable. I've spoken to Luis and it will be dealt with internally,” Rodgers says. “Diving is not something we advocate. Our ethics are correct.
“He has been totally understanding on where I am coming from as manager of the club. This is a big club and, whatever people do say goes around the world, and what was said was wrong and not acceptable. There is no-one bigger than the club or the club's image.”
Liverpool face Norwich tomorrow, and it will be interesting to see whether Rodgers drops the striker, or allows him to continue his impressive form against the Canaries.