"The baby is due around the time of this Test and, if I get a phone call, I'll be leaving the ground," Vaughan told British newspapers on Thursday.
Vaughan, however, will try to put it to the back of his mind if he is batting when he gets the call.
"If I'm out in the middle batting at the time, it's just unlucky," he said.
"The hospital (in Sheffield) is pretty close, which is a good thing. But perhaps I will have to make sure she 'drops' (the baby) before 11 in the morning."
New Zealand said England must abide by the regulations, which state a player who is off the field for a long period cannot bat until five wickets have fallen in his team's innings.
"England asked us two questions," said New Zealand manager Lindsay Crocker.
"The first was if we'd object to them using a substitute fielder if Vaughan left the ground. We had no objection to that."
"The second question was whether Vaughan could still bat in any position. But we said the regulations should apply, as they did in the first Test when (New Zealand's) Nathan Astle had to bat at number seven after being off with the flu."
Vaughan is due to bat at number four for England, who lead the three-match series 1-0.
