The South American nation secured a battling 1-0 win over Italy to snatch second place in Group D at the FIFA World Cup on Tuesday, behind surprise package Costa Rica, as they set up a last-16 class with in-form Colombia.
But Liverpool star Suarez found himself in the all-too-familiar position of being under disciplinary scrutiny after appearing to bite Juventus defender Chiellini amid a tangle with his opponent late in the contest.
The 27-year-old has twice previously received lengthy bans at club level for biting.
He first bit PSV Eindhoven midfielder Otman Bakkal during his time in Holland with Ajax in 2010, and he then sunk his teeth into Chelsea defender Branislav Ivanovic in a Premier League match last year.
After Tuesday's game, Chiellini claimed referee Marco Rodriguez saw the bite marks on his shoulder and urged FIFA to take action against Suarez, although the man at the centre of the flashpoint said he made no more than "contact with his shoulder" and suggested such on-field confrontations are nothing unusual.
"These situations happen on the field," Suarez told Uruguay's Channel 10, as quoted by the Daily Telegraph.
"I had contact with his shoulder, nothing more, things like that happen all the time.
On possible disciplinary action, he added: "I don't know anything, if FIFA analyse each case separately it's going to be complicated."
FIFA will wait to read Rodriguez's match report before deciding whether to take action against Suarez.
A FIFA spokesperson told Perform: "We are awaiting the official match reports and will gather all the necessary elements in order to evaluate the matter."
Uruguay captain Diego Lugano defended his team-mate, claiming "nothing happened", and went on to question Chiellini's conduct.
When asked by reporters about the alleged bite, he said: "What did you see? You saw this, really? You need to show me because I didn't see anything.
"Did you see it today or did you see what happened in other years. You couldn't have seen it today because nothing happened.
"The worst of everything is the attitude of Chiellini."
Italy manager Cesare Prandelli, who announced he would stand down after a game that saw his team eliminated from the World Cup amid a red card for influential midfielder Claudio Marchisio, gave a more understated assessment of events.
"I didn't see the images of Suarez but I did see the bite marks in Chiellini's shoulder," Prandelli said. "It is a shame, a real shame. The assistants of the referee were so busy, they didn't see anything."
Uruguay lost their opening game of the tournament 3-1 to Costa Rica, with Suarez unavailable as he completed his recovery from knee surgery.
Oscar Tabarez's team take on Colombia on Saturday with their talisman's participation thrown into doubt once more.
