"He bit me, it's clear, I still have the mark," Chiellini told Italian television station Rai after the match.
"The referee should have blown his whistle and given him a red card, also because he was simulating," added the Juventus player.
World governing body FIFA said they could not make an immediate judgement.
"We are awaiting the official match reports and will gather all the necessary elements in order to evaluate the matter," a FIFA spokesperson told AFP.
Italy crashed out of the World Cup as Uruguay's 1-0 victory, thanks to Diego Godin's late goal just after the biting incident, put the South Americans into the last 16 behind surprise Group D winners Costa Rica.
Italy finished the match with 10 men after Claudio Marchisio was sent-off for a stamp on Uruguay's Eligio Alvarelo.
But Italy felt Suarez, who twice previously has served lengthy bans for biting incidents, should have followed him down the tunnel after a controversial later incident.
Uruguay coach Oscar Tabarez said he hadn't seen it.
"I don't know, I don't have anything to say about it. During the game we're concentrating on other things," he said.
"It's a World Cup, we don't do cheap morality."
Suarez and Chiellini came together in the area, after which both tumbled to the ground, Chiellini holding his shoulder and Suarez his face.
The Italy defender stood up and pulled his jersey off his shoulder to show the alleged bite mark to Mexican referee Marco Rodriguez.
Meanwhile Suarez could be seen sitting on the ground holding his teeth.
Television replays suggested Chiellini was telling the truth.
If taken up by FIFA disciplinary chiefs it will almost certainly mean the end of the tournament for Suarez, painted as a villain at the 2010 World Cup for his deliberate goal-line handball which denied Ghana a famous quarter-final victory.
If Suarez is found guilty of another biting incident, it is inconceivable he will face anything other than a lengthy ban.
In April 2013, he was given a 10-match ban by the English FA after biting Chelsea defender Branislav Ivanovic in a match at Anfield.
- Sports & Recreation
- Luis Suarez
- Giorgio Chiellini