Mourinho initially set his sights on signing Atletico Madrid star Antoine Griezmann, but interest ended in him after he opted to stay in Spain.
But he is closing in on landing his alternative target with The Sun claiming the 24-year-old has agreed to sign on the dotted line.
It is said he has penned a five-year deal worth £350,000-a-week and personal terms have been agreed with the Real striker.
Morata will earn a staggering £90million in wages over those five years.
But The Sun say Real are playing hardball over the transfer fee for the striker.
The La Liga champions want to make a profit on Morata after buying him back from Juventus for just over £26m last summer.
Real chief Florentino Perez apparently wants the transfer fee to reflect the £90m wages he will earn at Manchester United.
And he has apparently told United chiefs that their willingness to pay £100m for Griezmann has set the bar for negotiations.
The La Liga champions have already rejected an opening bid of £65m for Morata.
But should United agree to pay a world-record £90m for him it would mean they would have shelled out an incredible £180m to broker a deal for Morata.
However, The Daily Star claim David De Gea could be key to securing the striker’s signature.
It is believed that Mourinho will offload Real’s top transfer target if they hand over Morata and pay an extra £45m for the keeper.