The Spain international is a target for Arsenal boss Arsene Wenger as he plots how to overhaul Chelsea at the top of the Premier League next season.
Manchester United, Liverpool and Inter Milan are also interested in the 27-year-old.
But according to reports, Pedro has emerged as an option for Blues boss Jose Mourinho.
Mourinho is set to sign a new contract until 2019 worth around £42million - or £200,000-a-week.
And when he pens that the Portuguese tactician will turn his attention to new signings, with a goalkeeper, defender, midfielder and striker on his radar.
Pedro has scored 10 goals in 45 games for Barcelona this season but has often been consigned to coming off the bench.
The speedy forward has been preferred to an attacking triumvirate of Lionel Messi, Neymar and Luis Suarez by Barca boss Luis Enrique and is apparently looking to leave the Nou Camp.