United have won each of their last eight matches, including six in the Premier League, to move to within three points of fourth-placed Chelsea in the table with a lot of football still to be played this season.
Even in Solskjaer's wildest dreams, surely the Norwegian would not have expected to be in this position when he replaced Jose Mourinho as head coach of United last month.
Solskjaer was brought back to Old Trafford with the view to improving morale in the squad, and while that has undoubtedly been the case, the results have been spectacular since he came through the door.
Friday's 3-1 win over Arsenal in the fourth round of the FA Cup made it eight straight victories in all competitions, including six in the Premier League to put United right back in top-four contention.
The 1-0 victory at Tottenham Hotspur on January 13 was followed by a 2-1 home success over Brighton & Hove Albion last weekend, which moved the Red Devils to within three points of fourth-placed Chelsea.
Even Tottenham Hotspur in third are now just seven points ahead of sixth-placed United, and the 20-time English champions are the overwhelming favourites to overcome Burnley at Old Trafford this week.
United will then travel to Leicester City and Fulham in their next two, before the small matter of the first leg of their Champions League round of 16 match at home to Paris Saint-Germain on February 12.
Under Mourinho, United were difficult to watch and were also not picking up results. It has been a total flip since Solskjaer arrived and it could yet be a successful campaign for the club.
That said, it is understood that there will not be an immediate decision made over Solskjaer's potential role beyond the end of the season, with the club expected to take their time when it comes to picking Mourinho's long-term successor having made too many mistakes in recent history.
Recent form: WWWWWW
Recent form (all competitions): WWWWWW
Burnley took a bit of a hiding at Manchester City on Saturday, suffering a 5-0 defeat to the Citizens in the fourth round of the FA Cup.
Head coach Sean Dyche made a number of changes for the clash at the Etihad Stadium and as expected, it proved to be a very difficult afternoon for the Clarets as they bowed out of the competition.
Burnley's recent league form is strong, however, having picked up 10 points from their last four matches. Indeed, they overcame West Ham United, Huddersfield Town and Fulham before picking up an impressive point at Watford on January 19.
Between October 6 and December 26, Burnley only picked up one victory. A 5-1 defeat at home to Everton on Boxing Day left the club in a very difficult position, but they have responded impressively in recent weeks.
It is a tough ask to expect Burnley to pick up a result at Old Trafford on Tuesday night, but they have a huge game at home to Southampton next weekend.
Six wins, four draws and 13 defeats - that is how Dyche's side have performed this season. A total of 22 points has left them in 16th position, just three points clear of 18th-placed Cardiff City after 23 matches.
Burnley have also already lost seven times on their travels in the Premier League this season, conceding 22 and scoring just nine, which is not a record that will fill the supporters with too much confidence.
Meanwhile, Burnley have only beaten United once since 1968 and have not been victorious in an away league fixture against the English giants since 1962.
Recent form: LLWWWD
Recent form (all competitions): WWWWDL
Chris Smalling is also back in contention for the home side after recovering from a foot problem.
Man United possible starting lineup:
De Gea; Dalot, Lindelof, Jones, Shaw; Matic, Herrera, Pogba; Martial, Rashford, Lingard
Burnley possible starting lineup:
Heaton; Bardsley, Tarkowski, Mee, Taylor; Hendrick, Westwood, Cork, Defour, McNeil; Wood
Head To Head
That said, Burnley have only beaten United once since 1968, while they have not been victorious away at the Red Devils since 1962, which is an indication of the task facing them on Tuesday night.
Dating back to 1892 when United were under the name Newton Heath, the pair have met on 127 occasions and the Red Devils lead the head-to-head record 61 wins to Burnley's 44.
We say: Man United 2-0 Burnley
It is difficult to imagine Burnley stopping the United train on Tuesday night. We fancy Solskjaer's side to make it nine wins in a row with a fairly comfortable home success.