French striker Edouard and Israel duo Nir Bitton and Hatem Elhamed are all absent having tested positive during the international break.
But Ryan Christie will return after self-isolating for two weeks, having being deemed a close contact of Scotland team-mate Stuart Armstrong.
“We are assessing whether he will be fit to start,” said boss Neil Lennon.
“Odsonne has had a cardiac screening and the blood tests and now we have to do some physiological work with him in terms of getting what the response to his heart rate is from certain exertions before we can clear him to train fully with us again.
“He is going through certain health and safety protocols at the minute.
Aside from Edouard, Bitton and Elhamed, wingers James Forrest and Mikey Johnston remain out.
So, too, does defender Christopher Jullien, with Lennon confirming he could be missing for several weeks due to inflammation at the base of his spine.
Patryk Klimala led the line in Saturday’s 2-0 defeat by Rangers, with Leigh Griffiths replacing the forward in the second half.
What do we know about Milan?
Milan are top of Serie A with four wins out of four but their path to the Europa League group stage was not so straightforward.
After a 2-0 win at Shamrock Rovers, Stefano Pioli’s side narrowly overcame Norwegian outfit Bodo Glimt 3-2 at San Siro, then squeezed past Portuguese hosts Rio Ave on penalties in the play-off round.
They scored in the 120th minute to force the shoot-out and captain Gianluigi Donnarumma’s fourth spot-kick save helped the Italians triumph 9-8 after 24 penalties in total were taken.
Veteran Swedish striker Zlatan Ibrahimovic has netted five goals so far this term, including both in Saturday’s 2-1 derby win against Inter.
What they said
Celtic manager Neil Lennon: “Christopher Jullien is going to be out for a period of time, he is still in a lot of discomfort. So he is going to be a few weeks, unfortunately.
“James has his foot out of the pot (boot) now so he will be scanned in the next couple of days. Mikey Johnston is back in training but he has been a long time out so it is softly, softly with him.”
- The sides have met 10 times in continental competition, all of them in the European Cup/Champions League. Celtic have won once – a 2-1 victory in October 2007.
- Celtic have won three of their past four Europa League home games – as many victories as they managed in their previous 10 such matches.
- Milan have won just one of their past four Europa League group stage matches (5-2 against F91 Dudelange in November 2018), conceding two or more goals in three of those fixtures.
- Milan’s Hakan Calhanoglu has been directly involved in 10 goals (5 goals, 5 assists) in his past seven Europa League games (including qualifiers).