Chiellini is reportedly on the summer wishlist of some of Europe's biggest clubs and the player and his agent have done little to curb the speculation.
That has died down in recent weeks during the World Cup but Italy crashed out of the tournament during the group stages and attentions have turned to domestic issues once again.
So, in a bid to stop the speculation developing further, Juvenus are prepared to offer Chiellini a new bumper deal.
General director Giuseppe Marotta told La Gazzetta dello Sport: "He has never been put on the market. We are ready to meet his agent and give him the financial recognition he deserves."
Marotta has also sought to play down any suggestion that experienced goalkeeper Gianluigi Buffon could leave Juve this summer.
He added: "I am very confident that he will stay. Gigi is one of us."
While Chiellini and Buffon are expected to still be at Stadio Olimpico next season, Mauro Camoranesi appears set to head for the exits.
The 33-year-old midfielder has spent the past eight years in Turin, but Marotta admits it is time for a change.
"We have explained to him that Juve will always be grateful to him but there comes a time to turn the page," he said.