The Belgian ace joined the Blues from Lille in 2012, and has been a hit in West London.
His form has been consistently good, but under the guidance of new boss Jose Mourinho he has recently moved up a gear with a series of fine displays across the hectic festive schedule.
His excellent performances have alerted PSG, who are ready to make a move to lure him back to Ligue 1.
The mega rich Parisians are unlikely to bid this month, and may instead wait until the end of the season to launch a big money raid.
The Parc des Princes side are no strangers to splashing the cash since their 2011 Qatari takeover, and are thought to be prepared to offer Hazard a massive salary on top of the large sum it will cost to convince Chelsea to sell.
The 22-year-old carved out his reputation in French football with Lille, and is still held in high regard over the English Channel.