Rulli has spent the last two seasons on loan at Real Sociedad and will be loaned back to the Basque club when Manchester City complete the deal.
The 24-year-old made 63 appearances for Real Sociedad in his two seasons at the club, conceding 73 goals and keping 22 clean sheets.
New Manchester City boss Pep Guardiola appears keen to bring in a new goalkeeper to compete with Joe Hart who had a poor Euro 2016 with England.
City were linked with Barcelona goalkeepers Andre Ter Stegen and Claudio Bravo but it now appears that Guardiola has turned his attentions to 24-year-old Rulli.
Standout matches today