The French winger became a father overnight and did not travel with Bayern earlier on Monday to Liverpool. Instead he will arrive later in the day, Kovac told reporters.
"He practically did not sleep so we will have to see," the coach said.
Bayern are already without defender Jerome Boateng but Kingsley Coman could get the green light to play after overcoming an ankle injury from Friday's win over Augsburg in the Bundesliga.
The speedy 22-year-old scored twice in that game before his late injury and the Bavarians desperately need his recent good scoring form against the Premier League club at Anfield.
"It is getting better by the hour," Kovac said. "He must be absolute pain-free to play and we are confident that our medical team can get it done for tomorrow."
Bayern are second in the Bundesliga behind Borussia Dortmund at the moment but they progressed to the knockout stage top of their Champions League group and unbeaten.
"Liverpool are a top side, but so are we," Kovac said. "They will also have respect for us. The aim is of course to progress. If Liverpool give 140 percent, then we need 150 percent. It will be a real battle."
The return leg in Munich is on March 13.
(Reporting by Karolos Grohmann; Editing by Amlan Chakraborty and Christian Radnedge)
