The Sun, as quoted by Metro, is reporting that the Manchester United boss is eager to get deals wrapped up as soon as possible.
The same article states that Solskjaer is eager to sign players from Premier League clubs in the bottom half of the table and even from Championship outfits.
According to the same story, the Red Devils manager is hoping to complete deals for Swansea midfielder Daniel James and Newcastle prospect Sean Longstaff.
The report goes on to claim that the Norwegian head coach wants Manchester United to bring in Norwich City youngster Ben Godfrey and Stoke City defender Nathan Collins.
The Sun report adds that Solskjaer has made it clear to Manchester United executive vice-chairman Ed Woodward that he wants these deals to be concluded swiftly.
Manchester United finished in sixth place in the Premier League table following a humiliating 2-0 loss to relegated Cardiff City on the final day of the season.
The Red Devils have made some poor signings over the past 12 months or so, including Chile international Alexis Sanchez and Brazilian midfielder Fred.
Manchester United have only managed to finish in the top four on two occasions in the past six seasons.
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