Newcastle value the talented 21-year-old at £50m but Manchester United feel the fee is overpriced for a player that has made just 13 senior appearances for the club.
The Red Devils have already had a £25m bid rejected as Ole Gunnar Solskjaer looks to fill the void left by Ander Herrera in his midfield.
But the Mirror say United are ready to test Newcastle’s resolve with a £30m bid as they look to make their third signing before the transfer window shuts on August 8.
Newcastle are keen to add to their own funds to help Steve Bruce land his targets and have already pocketed £30m from Ayoze Perez’s departure to Leicester.
The Toon will also look to how Crystal Palace played hardball over Aaron Wan-Bissaka.
The Eagles held out for £50m for their right-back and Newcastle know United will eventually pay big if they want to secure their transfer targets.
Meanwhile, Longstaff spoke out last week about rumours of a St James’ Park exit.
”I just keep my head down,” Longstaff said.
“I am just trying to get fit – that’s all I can focus on. I am still a Newcastle United player.”
Longstaff is currently recovering from a knee injury and is focused solely on being available for Newcastle’s Premier League opener against Arsenal on August 11.
He said: “I want to get back on the pitch as soon as I can. That is what I am looking forward to doing.
“I make more and more progress every day, that’s all I look forward to. I can’t wait to get on the pitch and impress the new boss.”
United’s opening fixtures sees them welcome Frank Lampard’s Chelsea to Old Trafford.