Solskjaer replaced Jose Mourinho in December 2018, originally on a caretaker basis.
A string of fine results, including a Champions League win over PSG, saw Solskjaer at the wheel permanently though the Norwegian seems to be under constant pressure.
A poor start to the Premier League season ramped up that threat, and Solskjaer knows that wins are the only way to ease the pressure.
He insists he has good contact with the likes of executive vice-chairman Ed Woodward and Solskjaer is open to anything.
He said: “For me, it's all about results and if we keep improving we have a very good opportunity because this team and this squad is going places.
“We live in a results business - and all I want is for Man United to improve as a team and as a club.
“I have very good dialogue with the club all of the time.
“You have to think long-term and short-term – and I would never ever think that this is my chance to prove a point and that's it's all about me.
“That's not what it's about here. Every decision I make is for the good of Man United.”
Former Tottenham boss Mauricio Pochettino has been linked with the job should Solskjaer depart, though the current United boss is not thinking about that.
The former striker added: “Teams that win the league put good runs together, consistent ones.
“If you look at the last 40 games with this team, we win two draw one, win two lose one. So we are becoming consistent.
“Since the Burnley game (in January), only Liverpool have taken more points, so we are getting there. We are getting better and better.
“We didn't start the league campaign on a par with everyone else, because of Europe and the pre-season we didn't have.
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“Now we're showing what we are capable of and if we keep improving and keep this mindset, I am sure we will move up.
“This season is very unpredictable and the main thing is making sure the next game is always the most important and that we don't take our eye off the ball.
“You can forgive any mistake as long as you have the right approach – and I feel we're getting there.”