Cech has had to settle for a place on the bench at Stamford Bridge this season as Thibaut Courtois took the No 1 jersey.
Arsenal and Liverpool are reportedly interested in the 32-year-old, who has made it known that he wants to play football more regularly.
But according to the Daily Mirror, the Ligue 1 champions have now entered the race for the Czech.
PA
Petr Cech has been second choice at Chelsea
They add that Chelsea boss Jose Mourinho is already looking for a replacement and has earmarked Fulham youngster Marcus Bettinelli as a possible signing.
However the Cottagers want to offer the England Under-21 international an improved deal to ward off the interest.
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