The Gunners knocked back Barcelona's £29million bid for Fabregas earlier this month and insist their captain, who is under contract until 2015, is not for sale.
The midfielder left the Nou Camp for north London as a 16-year-old in 2003 and played alongside Gilberto before the Brazilian joined Panathinaikos two years ago.
Barca boy: Fabregas has always said he will return to Catalonia - some day
Fabregas has made no secret of his desire to return home and Barca's chances of landing the Spain star increased when they elected Sandro Rosell, who is close to the player, as president.
But Gilberto said: 'I think he should stay. 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.'
Old pals: Midfield duo Gilberto and Fabregas played in the same Gunners side
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