The former Welsh winger would consider leaving if he is overlooked as Van Gaal's successor and United are wary of losing a long-standing link to past successes.
Mourinho had long been expected to take over this summer after six months off following his sacking from Chelsea.
In February, Inter Milan director Bedy Moratti, sister of the Italian club's former president Massimo Moratti, divulged that Mourinho was headed for United after having lunch with the former Inter boss and her family in the city.
Asked afterwards if the 53-year-old Portuguese coach will return to Inter, she replied: 'No, he's happy now, he's going to Manchester.
Of course, he's always fantastic and we missed him as a person here.'
As recently as last month, Mourinho confirmed that he would be back in management this summer but refused to confirm a destination despite saying he hoped to stay in England.
'I am not in position to turn down [jobs],' Mourinho said. 'I am in a position to analyse, this is April, everything starts in July, every decision is made between May and the start of June.
'I am not in a position to deny, I am open to any club, national team, but I have to be honest, if possible, a club.
'I would prefer [to stay England]. I love the country, the football here, my family is very stable and happy.'
