The lefty, who celebrated his 30th birthday on Friday, was in the hospital all day and night on Friday celebrating the birth of his first child, a baby girl, with his wife, Bobbie.
"I hope he's here today, but of course he didn't get much sleep because they were at the hospital all day yesterday and evidently it must've taken longer than they thought because I think she delivered at 2 a.m," Leyland said.
Leyland said he had seen a texted picture of Coke with his newborn but had not seen Coke in person at that point -- around 12:30 p.m. ET -- and Coke understandably wasn't yet in the clubhouse for the game, which started at 4:10 p.m.
But Coke normally pitches in the seventh or eighth inning, so he wouldn't be needed until later in the day, anyway.
"I'm hoping by the time he pitches, it will be about 6:30 or so," Leyland said. "I'm hoping he makes it, but I'm not sure if he would or not, to be honest with you."