Darome Jenkins hasn't contacted his family since around Christmas, Cullen said Wednesday.
"He went out to Hawaii (where he has a residence)," Cullen said, "and we haven't heard from him since he went out there. It's been a little over a month.
"Obviously, you're concerned for his safety, concerned about how he is, his state, everything. We've just got to wait and let it play itself out. There's nothing much I can do from right here."
Cullen and his older brother, New York Jets defensive tackle Kris, were raised by their father in humble circumstances in Ypsilanti, Mich., from the time they were toddlers.
Cullen, who has patiently answered questions about his father's disappearance this week, wouldn't go into why he was raised only by his father.
"Whatever happened with him and my mom, I'm not too sure about, nor do I really care," Cullen said. "I don't try to focus on that stuff too much. So it was us growing up. My dad, he worked a lot to take care of us. And he did a good job of it."
Cullen has a ticket to Sunday's game set aside for his father, but he's unsure if he will check with family members before the game to see if Darome is in attendance for the biggest day of his younger son's professional career.
"You know, it's a tough situation, but you've just got to try not to think about it too much," Cullen said. "Just focus on everything else and try to stay busy with everything else."