The two Barcelona keepers have shared the goalkeeping spot at the Spanish champions over the last two seasons but are said to be unsatisfied with the arrangement.
At 24, Ter Stegen would be the more expensive option but would also be avalable for the long term.
Bravo, at 33, would be the cheaper option and Guardiola would be happy to take either of Barcelona's goalkeepers.
This therefore leaves Joe Hart's future in doubt as Ter Stegen or Bravo would likely be the first choice keeper at City.
Hart had a disappointing Euro 2016 with England having made two mistakes leading to goals. The Man City stopper failed to save Gareth Bale's long-range free-kick, despite being hit fairly centrally in his goal.
Hart then failed to stop Iceland's winning goal in their 2-1 victory over England, even though it appeared a fairly routine save.
Should Joe Hart be worried?