The former Chelsea coach would be United's third manager in three years with the club having lacked stability since former manager Sir Alex Ferguson's highly successful 26-year-reign ended in 2013.
Ferguson's successor David Moyes was shown the door 10 months into a six-year contract while Van Gaal has come under fire for United's dour style of play under his guidance.
United's interest in Mourinho is a dramatic turnaround for the club that for so long resisted the temptation to sign the controversial former Chelsea coach.
"The fact that the club appear ready to compromise those principles and sign a pact with the 53-year-old Portuguese coach is not only a sign of how desperate things have become at Old Trafford but also how much United as a club have changed in a short space of time," said the Daily Mail.
However, other reports suggest Van Gaal is still a chance of remaining at Old Trafford, with his side's Champions League qualification prospects all important to him appeasing club owners and investors.
"That means Van Gaal must either guide United to a top-four finish in the Premier League or win the Europa League, which now carries a passport into Europe's top club competition," said the Mirror.