"The wife is due any day, so hopefully this baby can stay in until after the game on Sunday," Tillman said Wednesday on WSCR-AM 670. "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."
After practice Wednesday, Tillman downplayed his potential decision.
"Man, you all are looking too much into that right now," Tillman said. "Next question. You all are looking way too much into that."
Tillman, who has two daughters and a son, said the trials he and wife Jackie went through when daughter Tiana was born helped him realize that his family always comes first. Tiana was born with a form of cardiomyopathy, a weakening of the heart and its pumping system, that required a heart transplant in 2008.
"At the end of the day, that's all you have (family)," Tillman said. "This game is important to me, but after what we went through with my middle child (Tiana), to me football will always be second or third in my life. That was a great lesson learned to teach me that when I'm done playing football my family will still always be there for me."
Receiver Brandon Marshall credited Bears coach Lovie Smith with fostering a family-first attitude with his players.
"You take on the character of your leader, and Coach Smith since Day 1 in my own personal business, he's always preached family first," Marshall said. "So 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. It's a special group. Coach Smith is a special guy; definitely how he runs things. Like I said, you take on the character of your leader. That's what he preaches: Family comes first."
Tillman, the NFC defensive player of the month for October, is coming off a remarkable performance against the Tennessee Titans in which he forced a career-high four fumbles. He already has forced seven fumbles this season, and 36 in his career, which are the most in the NFL by a defensive back since 2003, when Tillman entered the league.
Bears middle linebacker Brian Urlacher, who was named defensive player of the week, wasn't aware that Tillman may not play.
"Why would he miss the game? Oh, his baby? Then we won't have him," Urlacher said. "Our backups are pretty good."
If Tillman is forced to miss the game, the Bears are expected to turn to veteran cornerback Kelvin Hayden to cover Texans wide receiver Andre Johnson. Hayden is familiar with Johnson from his days in Indianapolis where he played against Johnson twice a year in the AFC South. Hayden saw his role increase in the Bears' defense last week when he supplanted D.J. Moore as the club's primary nickel back in the team's road win in Tennessee.
Sunday's game features two 7-1 teams as well as two of the top defenses in the league. The Bears are second in the NFL in fewest points allowed; the Texans rank third.
ESPNChicago.com's Jeff Dickerson and Michael C. Wright contributed to this report.