Delph's girlfriend Natalie is due to give birth early next month and he is desperate to attend, but the 23-year-old admits he must remain committed to his duties for Villa.
The former Leeds man fears he cannot afford to miss a game at this vital stage in the season, with Villa just three points above the drop zone.
"We have spoken about it and we know it's a possibility," said Delph, who scored an own goal in Saturday's 1-1 home draw with Fulham.
"It could happen as one of the games is about to go on. But this is a crucial part of the season and if I'm down to play in the games, I need to be playing.
"Natalie appreciates the situation and is 100 per cent behind me.
"I want to see my baby being born and hope it happens. Ideally, it will happen on a Wednesday."