The Manchester City midfielder's wife, Natalie, is due to give birth on June 30, mid-way through the World Cup. The couples' due date is just two days after England's clash with Belgium, and two days ahead of the last-16 fixtures, should they qualify.
Delph told 'Sky Sports': ''We're not 100 per cent certain, [but] with a game on the 28th there might be an opportunity to fly back and then get back fast.''
''Gareth has been fantastic. There's nothing more important than family to me: family always comes first and always will. If I do have the opportunity to get back I will, but if not she's tough. She's a Yorkshire lass so she'll deal with it.''
As for his call-up, the 28-year-old said: ''I was over the moon, I was doing cartwheels. I'm a team player and I think the manager [Guardiola] values people like me, who pretty much put themselves last and put the team first.''
He added: ''Wherever I'm asked to play. I'm all about the team, I've been that way since I was a really young guy, and I'll continue to be that way throughout the rest of my career.''