The Argentina international has played a major part in helping the La Liga giants to success, winning 15 major honours with the club since joining from Liverpool in 2010.
According to the Gazzetta dello Sport, Barca's efforts in trying to sign Brazil defender Marquinhos means that the Bianconeri will step up their efforts to take Mascherano to Turin.
The 32-year-old has made 171 appearances for Barca and has earned 128 caps for the Albiceleste.