The Spanish international could be available following the signing of Turan as he is no longer guaranteed playing time at Barca next season.
Chelsea are in the market for new additions out wide having missed out on signing the Turkish international.
Turan has agreed to a five-year deal with the UEFA Champions League winners keeping him at the Camp Nou until July 2020.
The 28-year-old winger provided six assists and three goals in 46 appearances in all competitions for Atletico Madrid last season.
Pedro provided nine assists and scored 11 goals in 50 appearances for Barcelona last term.