Odom asked a judge Nov. 5 to set up a visitation schedule and establish "reasonable child support" for daughter Destiny, 12, and son L.J., 9, who live with their mother Liza Morales, 31, in Manhattan, The New York Post reports.
Morales said she's had to beg Odom to pay attention to the children in the past.
"Lamar basically checked out as a father four years ago," she told the Post. "They haven't had quality time in a long time."
The Post said Odom's petition in Manhattan Supreme Court comes as he and Kardashian, 26, publicly talk about the names they've picked for the babies they plan on having.
The newspaper said the pair are about to star in a reality show, spun off from the E! series "Keeping Up With The Kardashians," which will follow Khloe and Lamar as they try to conceive.
Celebrity Couples of 2014 [PHOTOS]