Delph's wife Natalie's due date is June 30, two days after England's final group game against Belgium in Kaliningrad.
England's support staff are ready to provide the player a plane to get home as soon as he gets word of an impending birth and then jet him back to Russia to rejoin the squad.
"Obviously I would have to get back to England and then get back again and obviously that it is not ideal but it is part of life," he said.
"We are about to have a third child and I am not about to miss it if I can help it but I want to get back as fast as I can – we will have to see."
If England finish top of Group G, they will have a four-day gap before their second-round match in Rostov-on-Don.
Should they finish runners-up, Delph will have an extra day to complete his journey, before the second-round match in Moscow on July 3.
Delph said his team mates are behind his plan which has been cleared with manager Gareth Southgate.
"They are fine about it, Gareth understands how important family is to me, he is the same as well.
"We have spoken about it – he was once at England camp and had to fly back for the birth of his child. He got back ten minutes before, he said. Hopefully I can do the same," added the versatile Delph, who is not expected to start England's opening game against Tunisia on Monday.
Delph said that he would have no hesitation in making the trip, even if he knew that he was due to start a game.
"Absolutely – we have got a fantastic squad, great players and if I am selected to play and then have to go back to see my family there are players more than capable of doing the job that I can do, if not better, so I am confident with that decision," he said.
(Reporting by Simon Evans; Editing by Christian Radnedge)
