By Paul Clennam
The England international midfielder is set to sign a contract worth £100,000 (€139,000) per week at the Etihad Stadium but the deal has taken extra time to complete as his wife is due to give birth.
As a result, Delph's capture from Aston Villa has not been concluded sufficiently quickly to include him in the City squad touring Australia.
The 25-year-old is aware that he will be a squad player under Manuel Pellegrini but has been told that he will get a similar number of opportunities to that enjoyed by James Milner over his spell at the club. Milner signed for Liverpool on a free transfer earlier this summer.
Delph is part of City's drive to recruit more home-grown players, with Milner and loanee Frank Lampard the only Englishmen to start more than 10 games across all competitions for them last season.
Villa, meanwhile, have already moved to replace their captain, confirming on Friday the capture from Lille of defensive midfielder Idrissa Gueye.