The London Evening Standard says the frustration over the time taken to conclude transfers has been felt among targets, as well as fans.
United have so far adhered to a one-by-one approach, leaving potential signings hanging on for deals to be struck.
Longstaff had hoped to be in place for the start of the tour – but a formal approach to Newcastle managing director Lee Charnley didn't come until last weekend.
Woodward was stunned to discover the Tyneside club's £50m asking price and made it clear it was well in excess of what United are prepared to pay.
While it's believed the valuation was a case posturing by Newcastle – United have ended up paying in the region double their opening offers for James and Wan-Bissaka.
The latter of those deals is said to be framing Charnley's expectations regarding Longstaff, who United hoped would be among the easier transfers to conclude during this window.