Chiellini was bitten by Suarez during Italy’s clash against Uruguay at the World Cup in 2014.
Suarez, who was given a four-month ban for the incident, apologised to Chiellini following the game.
Chiellini and Suarez are now set to become teammates as the Uruguayan striker is closing in on his switch to Juventus.
And according to La Gazzetta dello Sport, Suarez has already spoken to Chiellini ahead of his switch to the Serie A champions.
The report also claims that Suarez has called his Uruguay teammate Rodrigo Bentancur, who is also at Juventus.
In his autobiography which was released earlier this year, Chiellini insisted that he has no ill-feeling towards Suarez over the biting incident.
‘After a couple of days we spoke again on the phone and there was no need to apologise,’ Chiellini said.
‘I am a great son of a bitch on the pitch as well and I am proud of it: malice is part of football, I don’t even call it impropriety.
‘It happened, and this is his way of dealing with direct confrontations, and, if I can say it, it is also mine: he and I are alike and I like to face challenges in this way.
‘I admire his malice, if he lost it he would become a normal striker.’
Suarez has agreed a three-year contract with Juventus worth around £200,000 a week.