The 37-year-old is out of contract at Manchester City, but is seeing the season out with the Citizens still in the Champions League.
When City’s campaign ends, the Chile goalkeeper will almost certainly return to Spain with Betis.
Just ‘small details’ are remaining before a definitive agreement is reached.
A source from within the Andalusian club told ED: “We trust that Bravo will sign for us soon. There are only some small details left and we hope to settle them very soon.”
Bravo has spoken about wanting to work with Pellegrini, who left City just before Bravo joined from Barcelona.