Bravo made 32 league starts last season to help Barca defend the La Liga crown but faces stiff competition from Germany international Marc-Andre ter Stegen to be the team's number one.
"All I can say is that Claudio has given us a lot in the past two seasons and I hope he stays here. He is an important part of this team," Mascherano said.
Asked about the goalkeeping dilemma at Barca with both Bravo and the 24-year-old Ter Stegen eager to be Luis Enrique's first-choice, Mascherano said: "Both of them are great goalkeepers. "The ideal thing for us is to have both players continue."
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Bravo, who joined Barca from Real Sociedad two years ago, is under contract with the La Liga champions until June 2018.
Sky Sports has reported that the move might be delayed because of a knee injury to Ter Stegen, though a deal remained possible before the August 31 transfer deadline.
"Claudio is a great professional, he is one of the most experienced players in this team," Mascherano said. "However, I will understand if he decides to leave if he thinks that is the best decision for his career."
Mascherano also said he, too, had considered leaving Barcelona before signing a new contract extension last month that will keep him at the club for the next three years.
Mascherano, who was a reported target of Juventus, said: "At the end of last season I did reconsider. "I had doubts on whether I could still play in such a demanding club as Barcelona is."
"I'm grateful to the club that they still count on me. I've always felt appreciated. I think I can still help the club."
(Reporting by Adriana Garcia; editing by Clare Lovell)
