In an interview with the media in South America, Suarez admitted 'falling' during a match against Stoke in an attempt to earn a penalty.
Rodgers has responded by describing simulation as "unacceptable" and revealed the club is poised to take action.
"I think it is wrong. It is unacceptable. I have spoken to Luis and it will be dealt with internally," Rogers said.
"It is not something we advocate. Our ethics are correct."
Suarez was handed an eight-match ban last season for racially abusing Manchester United defender Patrice Evra.
On that occasion the Anfield club showed support for the player, but the Uruguay international is likely to be punished on this occasion.
In the extensive interview with Fox Sports Argentina the Liverpool forward repeated claims that he is treated differently by the media because of his South American background.
He said: "I don't listen all the nonsense some people say about me. I'm accused of cheating here. People say I throw myself all the time inside the box.
"They said that when we played against Stoke, for instance, and in that case they were right. I invented a foul because we were drawing and I wanted to win.
"Sometimes on the pitch I say to myself, "What have I done?" But the name of Suarez sells papers."
The Uruguayan was recently accused of deliberately handling the ball moments before his winning goal at non-league Mansfield in the FA Cup.
But he said: "I touched the ball with my hand accidentally, and I was criticised because I kissed my hand. I say to the media: you should talk more about football, not about other stuff."
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