Don't think there's any chance of him going before the end of the season. United may not be run very well but I doubt anyone there actually believed the fairytale of Solskjaer becoming the new Ferguson. He was signed permanently because he wouldn't kick off about half the squad being shifted to cut down on wages. Lukaku/Fellaini/Herrera etc may not be top class players but they are good enough for top 4-8 team. No serious manager would have accepted that squad in the state it was at the start of the season. Martial or Rashford get injured and the backup is a player who was 17 at the start of the season. Other first in line squad players Matic/Mata/Young/Jones well past it for a few seasons.
Despite everything they're still only a few points off top 4 so probably around where they expected to be.