Looking at the way things are going I don't think we can hope to mount a serious challenge. Before signings, what is needed is work on our style of play. Our passing, movement, pressing, forward play, ideas in the final third - all need to improve from what we have seen so far. These things take time as we have seen with Liverpool & City. It took Pep one season to get used the league, develop City's style of play & get the squad he wants (He had three transfer windows before his second season begin). At Liverpool it has taken almost 3 seasons. I would say that our squad is in a much better shape than Liverpool's was when Klopp joined, so Ole should be able to do it in one season.
At time of joining, Ole and Klopp's mandates were different too. Ole is under pressure to get us a top 4 from what was a near impossible position. With games coming in quick succession & injuries he hasn't had the chance to fully implement his vision. He tried in the beginning but the players started dropping like flies after a few games. A few like Herrera and Matic, who were essential to our early form under Ole, have been on and off. These six months is basically an assessment period to judge which of squad is up for it.
I know we all want, me included, for us to drop £300m-£350m and improve the squad in one go to mount a title challenge. Thinking about it, it may be an unrealistic expectation. £200m + money from sales should be a good starting point for Ole to start improving the squad. Getting four players - a top CB, a top RB, a dominant midfielder & a versatile attacker - would be a fine start. Four is a good number of players to integrate in the first team and get going.
This is my expectation from the summer window:
Sold/Let go - Valencia, Mata, Herrera, Darmian, Rojo & Bailly.
In - CB, RB, CM & AM (preferably someone who can play on the right)
Squad -
De Gea/ Romero / Grant
RB/Dalot Smalling/Lindelof CB/Jones Shaw/Young
Fred/McTommy CM/Matic
RW/Lingard Pogba/Pereira Martial/Sanchez
Rashford/Lukaku
For me the most essential signing for us is getting a dominant midfielder who can free up Pogba to play in attack. Pogba does well in the midfield but he is at his best when he has freedom to join the attack and get in the box at regular intervals. It's not a coincidence that our uptick in goals and assists has dropped off since he has had to move deeper.
That squad should be good enough for a top three position and a good run in the cups, imo. If we are lucky Rashford and Martial will have breakout seasons and we will be able to achieve more.