Fabregas had been the subject of a long-standing interest from the Catalan giants, who he left to move to London at the age of 16.
Gilberto Silva spent six years at Arsenal and played alongside the Gunners skipper as he was developing his game as a youngster.
The 33-year-old has since moved onto Greek outfit Panathinaikos while Fabregas has become one of the world's most revered footballers.
The loss of the Spaniard to Barcelona would be a big blow to Arsene Wenger's team, according to Gilberto Silva, and the Brazilian feels the 23-year-old would be better off staying at the Emirates.
When asked if Fabregas should stay at Arsenal, he told Sky Sports News: "I think so.
I hope he stays. He is a big person and must ask himself and think very carefully if he has to go or not.
"But of course the final decision (is something) he has to do. In case this situation happens, it will be a big blow for Arsenal.
"But let's wait and see."