The former Barcelona No1 is leaving City when their Champions League campaign concludes this month.
And Bravo has admitted his admiration for Betis in a fans chat on social media.
"Betis? It is an institution that has a great history in Spain, many fans; they are clubs that attract any player's attention," he stated.
"Imagine what Betis means now with a great coach like Manuel (Pellegrini)?"
Along with Bravo, Betis are also interested in Crystal Palace keeper Vicente Guaita.