The Red Devils have been linked with a move to sign the Newcastle youth product throughout the summer transfer window so far.
Manchester United were thought to have made an enquiry for the 21-year-old but Newcastle have quoted their rivals a £50m asking price.
Longstaff was introduced to the Newcastle first-team by Rafael Benitez, who left the Magpies earlier this month.
With Benitez out of the picture, Longstaff’s future has been a source of relentless speculation ahead of the new season.
Manchester United manager Ole Gunnar Solskjaer has been looking to target young British players this summer.
And ESPN reporter Ogden believes Manchester United will complete a deal for Longstaff before the close of the summer transfer window.
“I think they’ll still keep plugging away at that one,” Ogden said of the Longstaff deal on the Transfer Talk podcast.
“Newcastle have shown that they’ve got a few problems at the moment with the ownership, the manager change.
“Sean Longstaff is a player that has got potential.
“He’s a Newcastle lad so it will be hard for Newcastle to let him go.
“But I think Newcastle tend to sell when the price is right.
“I think at the moment we’re just seeing negotiation tactics.
“Newcastle are holding out for £50m – they won’t get that, nobody will pay that for Sean Longstaff.
“But I think United at some point will get their man.
“But again I expect it to run into the last week of the window.”
Manchester United started their summer spending with the £18m addition of Wales international Daniel James from Championship side Swansea City in June.
The Red Devils completed a £50m deal for England Under-21 international Aaron Wan-Bissaka from Crystal Palace earlier this month to bolster their defence.
Manchester United finished in sixth place in the Premier League table last term to miss out on Champions League football for the fourth time in six seasons.
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