FIFA's disciplinary committee met late into Wednesday night without coming to a verdict on the case of the Liverpool striker, who has been charged with misconduct for biting the Italy defender.
The hearing is continuing in Rio de Janeiro on Thursday with both the Uruguayan FA and Suarez having made their cases - in Suarez' case through a lawyer.
FIFA are expected to give an update on the situation at a media briefing due to be held at the Maracana at 2.30pm BST.
Suarez and the Uruguay squad are due to arrive in the city ahead of Saturday’s last-16 clash with Colombia.
Speaking on Wednesday night, Uruguay FA president Wilmar Valdez said: "We know they met for a long time but we don't know if that means a good or a bad situation. They will continue in the morning."
FIFA disciplinary panel member Martin Hong said: "We have to resolve it either today or tomorrow. It's our duty to see justice done."
Uruguay captain Diego Lugano has defended Luis Suarez and claims the incident with Chiellini was an isolated incident.
"The pictures don't show anything. They show an approximation," said Lugano.
“I think it's so, so clear, so evident, that it surprises me and I even find it funny the importance given to an isolated incident while nobody paid attention to much more potentially dangerous incidents for the health of players.
“I think that nowadays everything can be explained by what sells in football and the huge character of Luis Suarez."
Lugano believes Suarez is being singled out by the British media because he's such a special player.
"The British media has a vendetta against Suarez, and everyone knows that," he added.
"It's obvious the vendetta sells newspapers in England, otherwise you wouldn't be here. Uruguay and Italy played yesterday.
“On Saturday Uruguay plays Colombia, I don't know why there's a British journalist asking about Suarez."
Uruguay football federation president Wilmar Valdez has claimed Suarez was a victim of Italian aggression.
"When he falls, several substitutes insult him on the ground and some members of Italy's staff even came out of the bench to try to hit him," said Valdez.
FIFA's case against Suarez will be managed by a Swiss lawyer, Claudio Sulser, chairman of the FIFA disciplinary committee.
A former international forward himself, Sulser has worked for four years at FIFA, first as head of its ethics court.
Sulser can choose to judge the offence within the scale of typical red-card incidents: A three-match ban may then be appropriate, banishing Suarez at least until the World Cup final should Uruguay advance that far.
The maximum penalty would be a ban of 24 international matches.
FIFA can also choose to ban Suarez for up to two years. That would cover club and international games and would ruin a widely speculated transfer to Barcelona or Real Madrid.