Gudjonsson was on-loan at Villa for the latter part of last season from the Spanish club but although departing Villa boss Graham Taylor had been interested in signing him on a permanent deal, new boss David O'Leary has not showed any interest.
"Chelsea were strong candidates for the player but they failed to complete the transfer," said Real Betis president Manuel Ruiz de Lopera.
"I know Claudio Ranieri quite well and he's told me how disappointed he is with this outcome."