Solskjaer confirmed Bailly looks likely to have suffered a serious knee injury in Thursday's win over Spurs.
The Red Devils are negotiating a deal for Leicester defender Harry Maguire, but Solskjaer feels happy with his current centre-back stock.
"We've had six centre-backs rotating - and they've all done well," he told a press conference.
"Phil Jones played first three games, so it was his turn to be rested today.
"But of course, you're never happy when you get injuries. Let's hope it's not too bad for Eric."