Saints boss Carlo Ancelotti is a bag fan of the Italy international and should he remain at the helm at Parc des Princes, he will give his best to lure the defender to the French capital.
Tuttosport understands that the Saints are prepared to offer Chiellini a three-year contract worth €5 million per campaign.
Juventus are unlikely to be too keen on selling their prized asset, but a big money offer could change their minds.
The summer transfer window might be the last opportunity to earn a nice profit on the 28-year-old, while his departure would not create too many problems given that Martin Caceres and Federico Peluso are waiting in the wings.
Manchster City are also showing interest in Chiellini, but the Premier League champions have yet to prepare a concrete offer for the highly rated defender.