Anderson has emerged as a doubt for United's Barclays Premier League clash with Sunderland on Saturday.
The Brazilian midfielder was substituted during the second half of the 2-0 win against Otelul Galati and could miss the encounter with Steve Bruce's Black Cats, joining Chris Smalling, Ashley Young and Tom Cleverley on the sidelines.
Skipper Nemanja Vidic is available for domestic duty despite his European suspension but the boss is waiting for a clearer picture of the injury situation following the Champions League victory.
"Vidic will be back but maybe Anderson is the one player who picked up an injury last night," said the boss. "We'll see what he's like. He could be doubtful.
"There will be no returns for Young, Smalling or Cleverley though."
There is no update on Michael Owen after he was injured during the lead-up to Antonio Valencia's opening goal on Wednesday night.
"Michael injured his thigh when he made the run across the front post for the first goal," explained Sir Alex. "It's a killer for him. He started the season well, he's been training terrifically. His two performances in the League Cup have been great. He made the goal last night, no doubt about that. I hope he's not out for too long. We've assessed him this morning, he's had a scan but we don't have any results from that yet."
Michael Carrick returned to full training this week but Darren Fletcher wasn't available for the Galati game.