The Red Devils lost to Villarreal in the Europa League on Wednesday night after being defeated on penalties.
It means it is four years since the last time United won a trophy and the fans are not best pleased.
Solskjaer even mentioned after the loss to Villarreal that he was in desperate need of some players.
And he has reiterated that desire to the Old Trafford board with the Norweigan looking to improve all areas of his squad, including a striker and a centre-back.
According to the Guardian, he wants Harry Kane, Jadon Sancho, Pau Torres and Declan Rice.
All four would cost the club a pretty penny, potentially totalling up to £300m, while Solskjaer is also conscious of the fact that landing the quartet would be significantly difficult.
Of the four, Sancho is seen as the most achievable target with talks held in 2020 and Borussia Dortmund happy to sell at a cheaper price than last summer.
Kane, on the other hand, is on the other end of the scale with the price alone putting off United after Tottenham demanded at least £150m for the 27-year-old.
Despite the Spurs frontman looking to leave this summer, Daniel Levy does not want to sell the England international – while Manchester City are the favourites.
Torres played against United for Villarreal and has long been on the club’s radar while his fine performance in the Europa League final would only have convinced the transfer chiefs more over a deal.
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Meanwhile, Marcus Rashford has insisted United are determined to put things right.
He added: “People say a lot about Manchester United going downhill, blah, blah, blah, blah… but for me, the club, desire, hunger, talent, ability, the squad, we have everything to compete at the highest level.
“We just have to show it to the world and ourselves, show why we belong in the top places and why we need to win finals like this.
“Manchester City win the league, we finished second. Doesn’t mean nothing. Villarreal won the Europa League, we finished second. For us it’s nothing.
“I don’t want to hear ‘they were so close’ because it means nothing. One winner, one loser. Today we lost. We have to find out why and make sure next time we don’t lose.”