"It's all forgotten. I hope Fifa will reduce your suspension," the Italy player said in a Twitter statement released less than an hour after Suarez said he "deeply" regretted the bite and apologized to Chiellini.
Suarez, who received a hero's welcome when he returned to Uruguay over the weekend, said in a statement posted on Twitter: "I deeply regret what occurred. I apologize to Giorgio Chiellini and the entire football family...I vow to the public that there will never again be another incident like (this)."
Suarez, 27, sunk his teeth into Chiellini's shoulder during Italy's final group stage match against Uruguay last Tuesday, which saw the Azzurri crash out of the tournament after losing 1-0.
He was also suspended for nine games by Fifa and told to pay a €82,203 fine over the incident.
Uruguay's Football Association said last Friday it would appeal against the ban. Suarez originally denied any wrongdoing but his apology may now be taken into account by Fifa as it mulls an appeal.