Solskjaer's position as United manager is said to be under serious threat after Sunday's 2-2 draw at home to Aston Villa left the Red Devils ninth in the Premier League, a massive 22 points adrift of rivals and table-toppers Liverpool.
Villa captain Jack Grealish ran the show in the first half and capped a commanding performance with an equally-impressive goal, cutting in from the left to curl a shot over David De Gea, before Marcus Rashford's header just before half time hit the post and went in off goalkeeper Tom Heaton for an own goal.
Defender Victor Lindelof headed the hosts in front after the break but that lead lasted just four minutes as Tyrone Mings sprung the offside trap to volley home unmarked, claiming a share of the spoils for the visitors.
United's tally of just 18 points from 14 matches, their worst return at a similar stage since 1988-89, has left huge questions about how much time the Norwegian has left at Old Trafford as the pressure continues to increase with every game.
Since Solskjaer was appointed permanently at the Theatre of Dreams in March, the 20-time English champions have just six wins in 22 league matches and there are reports the club's hierarchy are contemplating a move for Mauricio Pochettino, who was sacked as Tottenham Hotspur boss last month.
Despite languishing down in ninth, United, who are winless in their last three games in all competitions, are only two points adrift of fifth-place Spurs and the two teams go head-to-head in a crucial clash at Old Trafford on Wednesday evening.
Speaking after the draw with the Villans, Solskjaer says he is not concerned about the club's position in the table right now and is more focused on his side produced good performances.
"I wouldn't have sat here and talked about us being fifth if we had got that one goal extra, so the league table at this point is not the biggest concern because it is so tight," he said.
"I just need to make sure that we get performances and get three or four performances after each other - and results."