Pedro was in and out of the Chelsea team under Antonio Conte last season, making only 17 starts in the Premier League, and his role at the club remains uncertain following the arrival of new boss Maurizio Sarri.
La Repubblica claims that Lazio are hoping to poach the Spaniard if he is forced to look elsewhere for more regular first-team football, with the Italian outfit reportedly lining up a £22m bid.
Pedro has just one year remaining on his contract at Stamford Bridge, and Chelsea could look to cash in on the 30-year-old this summer rather than losing him on a free transfer next term.
Sarri has been linked with a number of attacking options since his arrival at Stamford Bridge, including the likes of Dries Mertens and Jose Callejon from Napoli, which would further limit Pedro's first-team chances.
Pedro joined Chelsea from Barcelona in 2015 and has gone on to score 28 goals in 131 appearances for the club.