Although the club previously had little intention of making the Old Trafford legend permanent manager in December, he has proven so convincing that a series of key sources now see it as almost inevitable.
United officials have been especially impressed with the way Solskjaer has the major investments - like Paul Pogba and Anthony Martial - actually performing like world-class players who are now justifying their price, and more generally the mood around the club.
The feelings of happiness and progress, as well as positive media coverage and fan reaction, have also been influential.
Key to the thought process is also the knowledge that Mauricio Pochettino would be hugely difficult to get, but there is now more to it than that.
While the Tottenham Hotspur manager could cost up to £50m and then maybe require time to get a team together in the manner he likes, United have been impressed with how Solskjaer has adapted to what he has straight away, to the point where the latter is now almost being weighed up as a lower-risk situation.
Mike Phelan is seen as hugely important in that adjustment. He has “brought back the United way” at their Carrington base, but - crucially - that has allowed Solskjaer to be more focused on match preparation rather than training, and he is said to be exceptional at delegation.
That is something else that has drawn comparisons with Sir Alex Ferguson, who is another influential figure backing the Norwegian.
Solskjaer held discussions with officials in the last week, and The Independent has been told that talks have reached the point where potential summer transfer targets have been discussed, while he has also been looking at possible houses in the area.
United would prioritise a centre-half and right-back in the summer, while looking to move around four fringe players on to free up the squad.
While United do have a crunch period coming up - including Tuesday’s Champions League first leg against Paris Saint-Germain - Solskjaer has so generally impressed that these fixtures are no longer seen as gamechangers as to whether he gets the job.
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies