The Spanish international has found himself falling further down the pecking order at the Camp Nou with the big-money arrivals of Luis Suarez and Neymar over the past two summers.
Pedro is not satisfied with being a squad player at Barcelona and has asked the club to be allowed to leave in January.
Arsenal could offer the forward the chance to play first-team football that he demands and manager Arsene Wenger is known to be an admirer of the player.
The Gunners came close to signing Pedro in the summer, only for the deal to fall through, and Arsenal to end up bringing in Alexis Sanchez instead.
If Wenger is successful in bringing the forward to the Premier League he will have to fork up a fee in the region of £25million.