The Red Devils finished sixth last season, five points off the top four and 32 points behind champions Manchester City after a disappointing end to the campaign.
However, Solskjaer believes his side can at least start to bridge these gaps in the forthcoming campaign and a club like United cannot limit their ambitions to a fourth-place finish.
Weve got to aim for further up than fourth, weve got to, thats just being at Manchester United, Solskjaer told the BBC. Id rather be an optimist and be wrong than a pessimist and be right.
I cant say that these players wont be challenging for big trophies because they have the quality.
They do have the chance and we just need that consistency. We need a good start and we need to keep working every single day and not get our eyes off the targets.
Im not used to us being fifth or sixth, no, of course Im not. Thats where were at and thats the size of the challenge.
I love that challenge. Id rather make it “despite of” instead of “because of.”
Solskjaer famously made a sensational start to his career as Manchester United manager, but tailed off badly at the end of the campaign as their top four hopes slid away.
The Norwegian is aware that these wild swings in form need to be ironed out, and he plans to fix it in the short and long term at Old Trafford.
For me management is consistency, long-term but also you have to have short-term gains and results, continued Solskjaer.
No chance this is going to be about anything but improving the club and that we make steps closer to getting to the top, where we believe that we belong.
Uniteds pursuit of Leicesters Harry Maguire is continuing while the first team are away in Australia as part of their pre-season travels.