Solskjaer revealed that the trio had missed Saturday's FA Cup third round win over Watford after picking up injuries during the week. All three had started the midweek League Cup semi-final defeat to Manchester City.
The United manager did not specify their injuries but is hopeful that all three will recover in time for next weekend's trip to league leaders and reigning champions Liverpool, who his side will overtake if they avoid defeat at Turf Moor.
Pogba, Lindelof and Shaw may not be involved against Burnley, however, with their fitness to be assessed on Monday.
When asked if the trio would be fit to play both of this week's crunch league games, Solskjaer said: "I hope so. I hope all of them for Liverpool, definitely.
"I'm not sure if they’ll make the Burnley one. It's light training tomorrow then we’ll have to see on Monday."
Eric Bailly will also be assessed after being forced off during the 1-0 win against Watford. The Ivorian - likely to stand in for Lindelof in the centre of United's defence - suffered an apparent neck injury but later tweeted to confirm it was only a knock.
United have not sat at the summit of the Premier League table at this stage of the season since their last title-winning campaign in 2012-13, Sir Alex Ferguson's final year in charge.
Two wins would put Solskjaer's side six points clear of Liverpool having played the same number of games but the United manager insisted that it is still too early to consider this week pivotal to his side's title chances.
"We’re not even halfway through the season yet and every game in the Premier League is a challenge, it's a test," he said. "Every game is a different test.
"Watford today gave us a test. Burnley is a test, Liverpool is another, then you go to Fulham which is a different test again. No-one will remember how the league table looked like on 12 January 2021.
"We have good momentum. We started well again after the disappointment against City, bounced back really well with a win and of course we want to build momentum again.
"If we can get a win on Tuesday then when you win two games on the bounce again you can go into the next game confident. Every game in the Premier League is a chance to build some more confidence.
"I think it’s great that our fans are excited and they’re happy with where we are at and that we have this little sense of excitement. But then we’re not even halfway through the season, so of course every game against Burnley or every game against Liverpool matters a lot anyway.
"For me, all my eyes are on Tuesday and then let’s see where we’re at after that one."
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