After the success of the Lionel Messi, Luis Suárez and Neymar troika -- not to mention the recent signing of Arda Turan -- some players previously integral to the attacking success of Barcelona are supposedly looking for a way out of the club. One of them is Pedro Rodríguez, who's been with the club since 2004.
According to the not-so-reliable SPORT, Pedro has rejected previous offers from Arsenal, Liverpool and PSG; and now Chelsea are back in the hunt. SPORT have it that Pedro's would have liked to see out the remainder of his contract, but Turan's arrival from Atlético Madrid has made an already uncomfortable situation even more precarious. Any move would cost Chelsea €20 million.
Besides the general untrustworthiness of the Spanish press*, it's important to note that doing any deal with Barcelona is inherently difficult. Their transfer strategy might change significantly with their upcoming presidential elections (which is why Turan's deal is only provisional), and it's difficult to imagine them selling in such circumstances. Furthermore, Barcelona still are under a transfer ban and they won't be able to register new players until January next year. It's difficult to see Barcelona agreeing on a deal to see a player as useful as Pedro leaving the club when they won't have a replacement until the middle of next season.
*Especially when they're citing reports from England.
Verdict: Potentially interesting but not very likely.