"He can be one of the best players in his position. It's up to him," the Brazilian said. "Year by year, he's stepped up his quality."
He backed Fabregas and the rest of Wenger's young Gunners to move the club forward following Thierry Henry's Barcelona switch and promised to lead by example.
"Of course it's (Henry's departure) a big miss for us," Gilberto said.
"He was the leader of the team. He was the big player. But in football, you have to accept some things.
"We're still at the club. We are responsible for the club."