Globo Esporte says City are looking to solve their goalkeeper crisis by signing veteran Cavalieri.
Cavalieri was part of Roy Hodgson's Crystal Palace squad last season but didn't feature for the Eagles.
Pep Guardiola's team are in need of an experienced shot-stopper following Claudio Bravo's long-term injury.
The Chilean goalkeeper has travelled to Barcelona for scans after suffering a suspected Achilles tendon rupture in training on Monday.
And City are considering hiring free agent Cavalieri, who was also on the books at Liverpool but never featured there either.