The veteran attacker is off contract in June and preparing to leave London.
Pedro has opened the door to a move to Real Betis, however Sport says former club Barca could yet offer the player a return this summer.
Barca are having to work the Bosman market due to tight finances and Pedro represents value for money.
Over the weekend, Pedro stated: "I have to speak to the club, I have a contract until June 30. I am open to listening to other offers.
"Betis? I don't know, a meeting with Chelsea is pending."