Bailly, 26, has not played since the 2-1 win at Fulham three weeks ago and missed four of the last five games.
Paul Pogba‘s muscular injury that forced him off before half-time against Everton on Saturday was due to be assessed before the end of the weekend but he is unlikely to be available.
Harry Maguire has played in all but two of United’s games this season and has only been outright rested for the Carabao Cup win at Brighton in September. With an FA Cup quarter-final place at stake, Solskjaer could pick the club captain again.
“With Paul and Eric, I’m not sure if they’re going to be fit,” Solskjaer said. “I think Eric is closer than Paul.
“Of course, I think about if [Maguire] needs a rest. If he physically can’t keep going and going.
“Then, the nature of a centre-back position is a different position compared to full-backs or wide men or even centre midfielders, or any other position on the pitch. The centre-backs are the ones that you’re protecting mostly from the real fatigue because you’re working less.
“Then again, he’s never injured, Harry. He’s never been really badly hurt – touch wood – and hopefully he’ll be able to carry on.
“But, yeah, I’m not sure if he’ll play on Tuesday or not. I’ve not decided yet.”