United initially had a £52m bid rejected but are hoping a new offer of £60m will suffice for the Madrid board.
United also need somebody to replace the injured Zlatan Ibrahimovic after it was reported that he would be leaving Old Trafford.
It was believed that the Red Devils would had been prepared the break the world record transfer fee that they set last summer in an attempt to bring the French global to the Premier League.
Morata's return to the Bernabeu looks like it will be short lived.
Jose Mourinho seems to have other ideas, however, and the Swede is widely expected to be released by United in the coming days.
Mourinho certainly needs to add more goals to his team as they were the lowest scorers in the top seven last season and I think Morata will prove to be an excellent addition.
Unseeded Ostapenko tops Halep at French Open for 1st title
She added: "It's a tough day today because I couldn't win but let's work, let's keep working, let's believe". Meanwhile, the result means world No. 4 Halep won't overtake Angelique Kerber as the new world No. 1.
The 35-year-old has been offered the chance to complete his rehabilitation at the club.
Morata has only started 14 games for Madrid this season and is said to have found his lack of playing time extremely frustrating.
"Alvaro is a player who wants to play a more important role", López told Foot Mercato on Thursday.
Beyond that, however, it appears that the Merengues want to squeeze every cent out of their player.
Morata, 24, managed to score 20 goals for Zinedine Zidane's side last term despite being stuck behind Karim Benzema for the duration of the campaign.
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