City confirmed that he is not likely to be risked for the meeting in Germany, but midfielder Fabian Delph could be available for the first time since August.
"Fabian Delph returned to training ahead of City's trip to Monchengladbach, but Vincent Kompany looks set to miss out," the club said in a statement.
"The Man City skipper was forced off against Crystal Palace on Saturday after suffering from blurred vision and won't be risked in Germany.
"Delph hasn't featured for the first team since the end of August when he was an unused sub against West Ham. He required surgery on a troublesome groin problem and his return will give Pep Guardiola another midfield option."
John Stones, Ilkay Gundogan and Gael Clichy all took part in the session, after they missed the victory at Selhurst Park.
Yaya Toure - who scored both goals after being handed a surprise recall against Palace - also worked with the first team, although he is ineligible for the match.
A win for Guardiola's side will guarantee their place in the last 16 with one game to spare.