The Blues have been linked with the Argentine for some time, amid talk that he is no longer needed at the Parc des Princes.
Now it has emerged that talks between the two clubs are under way, with a fee of around £18m needed for the razor-sharp forward.
Jose Mourinho is known to be looking to add more guile to his attacking line this summer, and sees Lavezzi as the ideal man to compliment Cesc Fabregas and incoming Spain international Diego Costa.
Reports suggest negotiations are serious, with Chelsea ready to present the South American with a lucrative contract to move across the Channel.
The 29-year-old – who has also been linked with Arsenal – can play on either flank or in a central role, which may be of use to the Londoners.
Mourinho has already done business with PSG this summer by allowing David Luiz to complete a £50m switch, which may ease the process of nabbing Lavezzi.