The Gunners have been long linked with the 30-year-old midfielder but were unable to get a deal over the line.
It is now reported that the Portugal international could look for pastures new with Betis in need of funds to spend in the mid-season transfer window.
Arsenal are one of the top English sides interested in the Portuguese midfielder. Newcastle United and Leicester City are credited with an interest.
Arsenal head coach Mikel Arteta will be hoping that Carvalho can be lured to north London.
If the deal goes through, the midfielder would have to play second fiddle to Thomas Partey in the defensive midfield.