The former Aston Villa midfielder suffered a hamstring injury on his City debut in Melbourne on Tuesday following a challenge from Real Madrid’s Luka Modric.
City decided not to risk aggravating the problem by leaving Delph in Australia while the rest of the squad travelled to Hanoi.
Pellegrini said: “Fabian stayed in Australia as the doctor said it was not good for him to fly here. In the next 48 hours he will fly home then we will find the extent of the injury.”
City are now preparing for their friendly against a Vietnamese select as the team continues their preparation for the new Premier League campaign.
And Pellegrini plans to field a strong team including England international duo Joe Hart and Raheem Sterling.
“I think that for our team it???s an important game because we???re in pre-season and we???re near to the start of the Premier League ??? we have just two more games,” Pellegrini said.
“For our team, it???s very important to continue to improve in pre-season. We are going to have the best team we can put on at the moment.
“We have problems with some of the players but we???ll see Sterling, Joe and the other important players in our team with us.
“I don???t have any information about the Vietnamese team at the moment but tonight I will look into and then I will have plenty of information about the game.
“We will watch games they’ve played before ??? especially the one against Arsenal recently.”