This decision comes as Ederson's future at Manchester City is uncertain due to his recent high-profile mistakes and injury issues.
Ter Stegen, a 33-year-old German goalkeeper, is expected to leave Barcelona this summer after the signing of Joan Garcia from Espanyol.
Guardiola, who has managed Barcelona in the past, is reportedly seeking to bring Ter Stegen to the Premier League.
Barcelona is understood to be looking to remove Ter Stegen's high salary from their books, with Hansi Flick telling him to look for a new club.