Ole Gunnar Solskjaer's side could go top of the Premier League table for the first time this season by avoiding defeat at Turf Moor on Tuesday night.
The United manager revealed after Saturday's FA Cup third round win over Watford that Pogba, Lindelof and Shaw were doubts after picking up injuries last week.
But Solskjaer is now confident that Lindelof and Shaw will be available for selection against Burnley, while Pogba and Bailly will be assessed again after taking part in sessions on Monday.
"All of them trained today," he said. "Paul and Eric didn't do all of it but Luke and Victor did, so I've got a decent amount of players to pick from.
"Let's see with Paul and Eric how they are tomorrow."
Solskjaer has consistently played down talk of a title challenge from Old Trafford this season, insisting that it is too early to make predictions, and stuck to that line on Monday.
"We are better off this season than last season compared to the same time last year. We've won more games, scored more goals, played better football.
"That's a positive but as I said no-one remembers January league tables. For us it's just about developing this team and improving.
"I think we've shown again we can bounce back after disappointment. I thought the lads who played the FA Cup game showed good character, attitude and quality."
Join our commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies