Sky Sports is reporting that Manchester United want to sign the 21-year-old to bolster their midfield options ahead of the new season.
The same article states that Red Devils boss Ole Gunnar Solskjaer is a big admirer of the Newcastle youth product.
According to the same story, Newcastle will ask for around £50m to sell Longstaff to Manchester United this summer.
Manchester United have already signed two players in the summer transfer window as Solskjaer looks to rebuild at Old Trafford.
The Red Devils snapped up Wales international Daniel James in a £15m deal from Championship side Swansea City last month.
The 20-time English champions finally secured a deal to sign England Under-21 international Aaron Wan-Bissaka in a £50m deal from Crystal Palace last weekend.
Manchester United have a lot of work to do to catch up with Manchester City and Liverpool FC in the Premier League next term.
The Red Devils finished 32 points adrift of the Premier League champions to highlight the widening gap between the two clubs.
Manchester United failed to qualify for the Champions League for the fourth time in six seasons last term.
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