The Red Devils have been heavily tipped to sign Jadon Sancho, while his Borussia Dortmund team-mate Erling Haaland is also on the radar.
But Solskjaer is also hoping to keep some of his current players at Old Trafford as he bids to make up ground on local rivals and recently crowned champions Manchester City.
Speculation continues to swirl around Paul Pogba’s future, while Alex Telles has been linked with an exit less than a year after signing from Porto.
And there’s news on both as Mirror Sport looks at the latest transfer gossip from around Old Trafford.
United ‘close in’ on Sancho deal
United are reportedly closing in on a deal to sign Jadon Sancho – but could miss out on Erling Haaland.
According to The Times, Solskjaer’s side are close to finalising a £100m deal to sign Sancho from Borussia Dortmund.
A fee of £80m will be paid in instalments, with an additional £20m potentially coming later as add-ons.
The report claims Chelsea are in talks to either sign Haaland this year – or to set up an agreement which would see Dortmund keep him for another 12 months before a switch to Stamford Bridge.
It is claimed that a move to Chelsea appeals to the striker – but that he could change his mind if either of the two Manchester clubs or Real Madrid make a big-money bid.
Still hope on Pogba deal
United haven’t given up hope of convincing Paul Pogba to sign a new deal this summer.
Pogba is about to enter the final year of his contract at Old Trafford – meaning Ole Gunnar Solskjaer’s side could lose him for nothing in a year’s time.
But according to ESPN, there has been no firm contact from any of Europe’s major clubs, and there are doubts over whether the likes of Madrid, Barca and Juve could finance a deal.
However, the publication says United are still hopeful he will sign a new deal which would prevent him from leaving on a free transfer next summer.
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Telles given verdict on loan prospects
United have reportedly ruled out a loan switch for Alex Telles next season.
Telles was signed last summer to provide competition at left-back – and his capture had the desired effect, with Luke Shaw turning in his best season yet for the Red Devils.
But Shaw’s excellent form limited Telles to just nine Premier League appearances following his £15million move from Porto.
That has seen him linked with a move this summer – but according to A Bola , United have told the defender they are counting on him for next season and that any departure would need to be permanent.
The Portuguese publication claims Telles is willing to fight for his place – which will be a welcome boost for Ole Gunnar Solskjaer’s side.