The Swede would be returning to his former club, where he starred for two seasons from 2016-2018.
But the 39-year-old was substituted in the second half at the Stadio Olimpico on Sunday, with Rafael Leao replacing him after 56 minutes in the 2-1 victory.
Ibrahimovic, who has been integral to Stefano Pioli’s side this term with 16 goals in 22 games as they mount a title challenge, has now undergone tests.
Ibrahimovic has picked up a left adductor issue, which has come with an estimated three-week absence.
United welcome the Italians to Old Trafford for the first leg on 11 March, and Ibrahimovic could struggle to make the second leg, too, back at the San Siro on 18 March.
Ibrahimovic will undergo a second exam in 10 days, with reports suggesting the earliest a return could come would be the home leg against United.
That means Milan will also likely be without Ibrahimovic for crucial Serie A matches against Udinese, Hellas Verona and Napoli, with four points behind rivals Inter at the top of the table.
Ole Gunnar Solskjaer admitted he was impressed with the longevity of Ibrahimovic’s career after being drawn with Milan.
“We do have the tradition of making it hard for ourselves in draws,” said the Norwegian.
“It’s one of the those draws again that you feel could be a Champions League game. It’s good for us to have these games to look forward to. This team needs challenges and we enjoy challenges and we embrace them.
“The tradition and history of AC Milan, it’s a great club that we welcome and it’s a great stadium that we go to there, and we’re looking forward to it.
“Zlatan, of course, I’ve been so impressed, I’ve got to say, by how his career has gone. He had a career-threatening injury when he was here but came back from that and went to [the] MLS, then came back to Milan and has really lifted them.
“They’re on the up and have done really well this season. I’ve been so impressed by him.”
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies