The Liverpool forward was handed a four-month ban from all football activity as well as a nine-match international suspension for the incident which took place during Uruguay's 1-0 victory over Italy at the FIFA World Cup.
Suarez's punishment means he cannot play any club football until the end of October, but the 27-year-old would be able to undergo a medical should his reported switch to Barcelona materialise.
Claudio Sulser, head of FIFA's disciplinary committee, confirmed the appeal, and he stated that the sanction was "justice" for a "very severe case".
"The player cannot have any activity related to football, but a medical examination for a transfer, yes - the sanction is not linked to transfer rights," Sulser said.
"This is still an ongoing case and an appeal has been filed, so I prefer not to give my opinion.
"When the committee was analysing this case, one thing I mentioned in my capacity as the chairman is we don't need to impose an exemplary sanction, we need to have justice and reached the sanction in a very severe case."
Sulser was also questioned on why a punishment was handed out that also affected Liverpool, despite the misdemeanour happening during an international tournament.
"That's your opinion," he answered in reply. "It's a sanction against the player. That is the risk if you are a player and you are sanctioned at the World Cup.
"I agree with you it's a problem for Liverpool, but the sanction is in the disciplinary regulations."
The Chiellini incident marks the third time that Suarez has bitten an opposition player following clashes with PSV midfielder Otman Bakkal in 2010 and Chelsea's Branislav Ivanovic last year.
