Tillman told Chicago radio station WSCR-AM that he might not be available because his wife, Jackie, is due to give birth to a girl - the couple's fourth child. Their daughter, Tiana, needed a heart transplant a few months after she was born in 2008.
"The wife is due any day, so hopefully this baby can stay in until after the game on Sunday," Tillman said on the radio. "I hope she stays in - I'm having another girl. Monday, for sure, but if she comes Sunday, I think I'm going to have to be at the hospital Sunday. So, I hope she stays in until after Sunday."
Tillman wasn't in the mood to discuss his plans after Wednesday's practice.
He did, however, say: "To me, this game is important to me, but after what we went through with my middle child Tiana, to me football is second. It'll always be second or third in my life. That was a great lesson learned, to teach me that family - when I'm done playing football my family will always be there for me."
Asked about Tillman possibly missing the game, coach Lovie Smith said he tells his players, "'It's family first. If there is something you feel like you need to do for your family always do that.' How we look at it is like an injury. If a player can't go, it's next guy up. We'll keep going."
Tillman is making a case for defensive player of the year, and he forced four fumbles last Sunday at Tennessee. His teammates on the NFC North leaders expressed their support for him before practice on Wednesday. Tillman was not available for comment.
"You take on the character of your leader," receiver Brandon Marshall said. "Coach Smith since Day 1 in my own personal business, he's always preached family first. Whether I had to go out of town in OTAs to visit a family member or do something with family, it's no argument. It's take care of your family.
"We understand how things are run around here. This is a special group. Coach Smith is a special guy, definitely in how he runs things, and like I said you take on the character of your leader. That's what he preaches - family comes first."