The publication also claims that Sir Alex Ferguson is advising the club on the situation and could, once again, have a huge influence on any potential changes.
Elsewhere, the Sun says Van Gaal has been provided with extra security which could remain in place until United's next home game against Chelsea on December 28 - if the former Netherlands coach is still in charge.
But the biggest news on the managerial situation comes from the Daily Star who claim Mourinho is ready to move on from the disappointment of leaving Chelsea.
According to the Star, the Portuguese is desperate to takeover from Van Gaal and is willing to accept a four-year deal worth around £6million-a-season.
This would amount to a £16million pay cut, but one of the major stumbling blocks could be the future of Ryan Giggs as assistant boss with Ed Woodward reportedly agonising over the Welshman's position.