Barcelona will be considering a list of offers from clubs to help Neto secure a new home within the next week according to Diario Sport.
The Brazilian goalkeeper had already rejected an offer from Celta but offers from Fulham and Napoli are on the table.
The goalkeeper is keen on a move to Napoli. He already has experience in Serie A and would choose the Italian side over a Premier League move.
Barcelona are currently on a pre-season tour of the United States but Neto as well as other for-sale players like Riqui Puig, Oscar Mingueza, Martin Braithwaite and Samuel Umtiti are back at the Ciutat Esportiva to find a new club.
The 33-year-Old was born in the Brazilian state of Minas Gerais.
He began his career with Cruzeiro before joining Athletico Paranaense, coming to Europe in 2011 with Fiorentina. After four years there he spent two seasons with Juventus before coming to Spain to join Valencia. He joined Barcelona back in 2019.