Off contract in June, Pedro is weighing up his options ahead of the summer market.
And Gazzetta dello Sport says the former Spain international isn't short of offers.
But Lazio have now come forward with an approach to open pre-contract talks with Pedro's minders.
Speaking on Spanish radio last week, the 32-year-old reportedly said he plans to "terminate" his contract at Chelsea this summer.
But the former Barcelona man insists he was mistranslated, and instead wants to stay at Stamford Bridge beyond this season.
"As many people know, my contract is up in May," the winger told Chelsea's official website. "But I still haven't spoken to the club about whether or not it will be renewed and whether I'll carry on.
"I've seen loads of messages from Chelsea fans saying goodbye and thanking me for the time I've spent here, which I appreciate, but I'd like to tell all the fans simply that my current contract is coming to an end but I still have to talk to the club.
"I don't know whether I'll keep playing here or not. That conversation is still to come. But I have not signed for any other club. I belong to Chelsea. I have a contract. My wish is to be able to stay here but obviously we don't know what will happen. I have to speak to the club and let's see what happens."