The United boss said all three suffered knocks in the last five days - defenders Jones and Smalling during last Sunday's draining FA Cup win over Manchester City, while midfielder Anderson acquired his problem in training.
"We've got one or two doubts for tomorrow," said Sir Alex at his pre-match press conference.
"Smalling and Jones picked up knocks in the derby. We'll see what they're like tomorrow. Anderson got a knock in training, but hopefully he'll be okay.
"So we've got a reasonable squad for tomorrow. And we need a good performance against a team that will battle for everything. Any team near the bottom of the table will do that, as we experienced at home to Blackburn. We went into the Blackburn game with respect for them but it wasn't a great performance.
"We have to address Bolton's challenge properly. It's a local derby too, which adds something to it."