Sport says the Brazilian keeper is fed up of playing second fiddle to German international Marc-Andre Ter Stegen.
And it is claimed Neto, 31, has handed in a transfer request days after being linked with Mikel Arteta's Gunners.
Neto is understood to have a staggering £177m release clause included in his contract.
But Spanish reports say that Neto has pleaded with Barca to lower his price tag making it easier for him to depart.
And the Catalan Giants are understood to be open to letting the once-capped Brazil interntion leave the club.