The game’s global governing body say they are dealing with the incident as a matter of urgency – Uruguay’s next game is on Saturday - and that Suarez could face a worldwide ban if found guilty.
FIFA’s disciplinary committee were due to meet on Wednesday evening to look at the case – although they may not make an immediate decision.
"The Disciplinary Committee understands the urgency of the matter," said FIFA spokeswoman Delia Fischer.
"It is working to get and assess all elements in order to make a decision as early as possible, particularly given the fact that Uruguay are still in the tournament."
The longest ban in World Cup history was eight games for Italy's Mauro Tassotti for breaking Spain's Luis Enrique's nose with his elbow in 1994.
Suarez has twice been banned for biting opponents - for 10 matches in 2013 for his clash with Chelsea's Branislav Ivanovic and in 2010 he was given a seven-game ban while playing for Ajax for sinking his teeth into PSV Eindhoven's Otman Bakkal.
FIFA's disciplinary code allows action to be taken retrospectively via video evidence even if the incident has been seen by the referee – and they have the power to implement a worldwide ban.
Speaking after Uruguay’s 1-0 win over Italy last night, Suarez said he had been hit in the face - but that “these things happen on the pitch” and were not important.
"These kind of matches have these things, there is a lot of wearing out, and we need to give the maximum,” he said.
"It was complicated, they control the ball very well, it was very hot, we had to be cautious because of many players in the midfield that controlled the ball really well, but well, we controlled the timings, and that was important"
"Yes, I have been hit, near the eye, but those things happen in the pitch"
"Well, we are all football players, we all know what happens on the pitch, it's not important"
"I don't think it was important, those things happen on the pitch..."
Chiellini, who tried to show referee Marco Rodriguez the mark on his shoulder, believes the authorities must now look back at what happened and punish Suarez.
The defender told Sky Italia: "Suarez has bitten me and the referee saw it, but then there is the need to have the courage to take decisions.
"We will see if there is the courage to utilise the TV images to ban him."