The 27-year-old is currently playing second fiddle to Gianluigi Buffon in Turin and he is hungry for more action.
That, according to reports in Italy, has alerted both Everton and Lazio, who are keen on signing the Brazilian.
Lazio have held an interest in Neto since the summer and they are prepared to part with around £6m to secure his services.
Everton, meanwhile, are also on the hunt for a long-term goalkeeper after Tim Howard joined the Colorado Rapids.
Juventus are reportedly respectful of Neto’s desire to gain first-team football and will let him go if a suitable replacement can be found in January.