Baningime appeared to pick up a knock during Saturday’s Scottish Cup defeat by Falkirk while McInnes revealed fellow midfielder Tomas Bent Magnusson was “a wee doubt”.
“We’ve got a few concerns,” said the manager. “We’re still hopeful that we can get one or two. Ageu and McEntee will hopefully get back on to the training ground on Friday and train fully.
“It’s been a tough week. You’ve got to be grateful that you’re in a January window and you can still act upon it. At least we’re actively trying to alleviate some of the concerns we have and hopefully that can be the case.
“We’ve still got a lot going for us in the squad. I need to stress that.”
Asked if he would consider playing players out of position to fill midfield gaps, McInnes said: “You’ve got to look at everything.”
Hearts confirmed on Tuesday they will have to do without captain and Scotland striker Lawrence Shankland for up to eight weeks after the 30-year-old went off with a hamstring injury against Falkirk.
Elton Kabangu, Pierre Landry Kabore and James Wilson are available, along with regular forward Claudio Braga, while a deal has been agreed to sign Uganda striker Rogers Mato, 22.
“We’re hoping we can get Mato in for the weekend but if not at least we know he’s coming this month, which is good work by the club that we’ve negotiated that,” McInnes explained.
“He’ll definitely help us in the second part of the season.”
