Manchester United are facing the prospect of having to sell players in order to fund transfers beyond a deal for Jadon Sancho.
United are still eager to sign Borussia Dortmund star Sancho, who would cost around £108m.
As reported by the Evening Standard, if United want to secure further deals then they will have to raise funds by selling players.
The report states that the £46.5million signing of Bruno Fernandes from Sporting Lisbon in January came out of United’s summer budget.
Solskjaer wants to make further additions and is targeting a centre-back and a midfielder.
Speaking after United’s Europa League exit against Sevilla on Sunday, Solskjaer said: ‘It’s going to be a strange summer. The market is open for so long. We’ve got to be good, smart and clever.
‘We’re looking at it. I can’t say when and if they’re going to be done. It’s a quick turnaround. We have to be 100 per cent sure when we make those deals.
‘We definitely need to improve if we want to move up the table and on in the cups. We are working to improve what we have. We’re always looking to improve the squad.
‘It’s not about marquee signings, it’s about quality. You need the right personality to make us better. We might look at it today and see where we need to improve. Maybe today showed that they have to learn and get the consistency.’
With the financial impact of the coronavirus pandemic taken into consideration, United will have to work hard to increase the amount that they have to spend.
Chris Smalling, who spent the season on loan at Roma, is one player who could depart.
Marcos Rojo, back from a spell with Estudiantes, could also be sold.
Other players who could see their time at United come to an end include Jesse Lingard, Diogo Dalot, Phil Jones and Andreas Pereira.