Hart is set to join on a season-long loan, although it is understood West Ham will have an option to buy the England international next summer.
The 30-year-old spent last season on loan with Serie A side Torino, having been deemed surplus to requirements at Manchester City following the arrival of manager Pep Guardiola.
City signed Claudio Bravo as their presumed No 1 'keeper following Guardiola's arrival and this summer they have added Brazilian Ederson to their goalkeeping ranks.
