Suarez admitted to "falling" during October's goalless draw at Anfield in an attempt to win a penalty.
Reds boss Brendan Rodgers on Thursday described diving as "unacceptable" and revealed the club would look to take action.
"I think it is wrong. It is unacceptable. I have spoken to Luis and it will be dealt with internally," he said.
"[Diving] is not something we advocate. Our ethics are correct."
Suarez made the admission to Fox Sports in Argentina, saying: "Football is like that. Sometimes you do things on the field that later you think 'why the hell did I do that?'
"I was accused of falling inside the box in a match, and it's true I did it that time, because we were drawing against Stoke at home and we needed anything to win it.
"But after that everybody jumped out to talk - the Stoke coach, and the Everton coach... I understood that the name Suarez sells (papers)."
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No spot-kick was awarded to Suarez, who has previously been derided in England for his perceived theatrics. Following the Anfield match Stoke boss Tony Pulis hit out at the Uruguayan, labelling him "an embarrassment".
Jim Boyce, Britain's representative on FIFA, later described Suarez's dive as "nothing less than cheating", adding that simulation was a "cancer" in the game.
Suarez was back in the spotlight recently following his handball in the build-up to his winning goal against Mansfield in the FA Cup third round.
There were questions as to whether the 25-year-old handled the ball deliberately or if it was accidental.