McVeigh's wife Leanne is due to give birth next Tuesday - five days before the game against the Dogs - but the Bombers midfielder is aware all might not go to plan.
"We're very, very excited and we can't wait, so hopefully it comes at the right time," McVeigh said at the Bombers' family day, which drew a big crowd to Windy Hill on Monday afternoon.
But as for having to make a decision about playing footy or being at the birth, the 30-year-old said: "I won't be playing footy, mate. I'll be at the birth of my first child.
"It's a fairly slim chance [that I'll have to make the decision], but it has happened before. We'll be right. We'll assess it as it comes.
"It's round one, and there's a lot of footy to go, so it might help having a bit of a break."
The club insists it won't be pressuring McVeigh to play against the Bulldogs.
"Hopefully it doesn't clash but if it does we'll be respectful of whatever Mark's wishes are," football manager Paul Hamilton said.
"We understand that it's their first child and every birth of a child is just so important.
Hamilton joked that at least McVeigh wasn't having to make such a decision during finals time.
"We have told our players to make sure they don't have babies in September," he chuckled.
Mark McVeigh is a $256,300 midfielder in the Toyota AFL Dream Team competition
