The Sun says United were ready to offload Lingard for as little as £20million this summer when they agreed to let the attacker play for West Ham.
But his form since then — scoring five in seven appearances — has seen him rocket back into contention for a place in England's Euros squad.
And that is now forcing United bosses to consider almost doubling the price.
That causes a problem for West Ham because they were unable to secure a guaranteed option to make his loan deal permanent during negotiations.
And if his fee climbs towards £40m, it may be too much for them to pay.
There is hope that the 28-year-old has enjoyed himself so much at the London Stadium that he tells United he wants to make the move there on a full-time basis.
But Lingard will have little control on any fee United demand.