Ange Postecoglou is understood to be keen on a reunion with the Brighton keeper having named him his Australia first choice at the 2014 World Cup.
Ryan is in the final year of his contract with Brighton and spent time as backup at Arsenal last season, making only three league starts.
Spanish newspaper El Diario Vasco report he will be named as replacement for departed Miguel Angel Moya, initially on-loan with an option to make the move permanent.
Ryan already spent two years in Spain with Valencia from 2015 and the Premier League club are happy to let him leave England's south coast.
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