Van Gaal is desperate to see out the final 12 months of his current deal and leave Old Trafford on his own terms.
But senior bosses at United know the club needs someone of Mourinho’s stature to take on old rival Pep Guardiola, who will be in charge of City next season.
Meanwhile, Bournemouth boss Eddie Howe reckons Van Gaal has actually improved United this season.
Howe said: “He has done well overall when you look at the season. He has stabilised the team and moved the team forward.”