City have had a £2.6 million bid rejected by the Italian club, who want £4.4m for the former Liverpool keeper, sources said. However there is expectancy that a deal can be reached in the next few days for the former Spanish international.
A deal will cast doubt over the long-term future of Claudio Bravo. City have already spent £34.7m on Benfica keeper from Ederson and Reina is expected to become his backup.
That could mean that Bravo is forced to look for a new club fewer than 12 months after City signed him for £14m from Barcelona.
The Chile international has not travelled with the first team on their preseason tour to the United States after being given extra time off for playing at the Confederations Cup, where he was the hero in his country’s semifinal victory over Portugal on penalties.
But Bravo had endured a miserable first season at the Etihad Stadium, where he faced intense criticism and was dropped shortly after the turn of the year, with reserve Willy Caballero taking his place.
Caballero has since joined Chelsea on a free transfer after his contract expired at the end of the season while another City keeper, Joe Hart, is set to leave on a second season-long loan to West Ham United.
If a deal goes through, Reina would become the third keeper to join City since Guardiola took over the club last summer.