The Real Madrid striker has been heavily linked with a move to Old Trafford this season.
Starsport understands United boss Jose Mourinho is a huge admirer of the 24-year-old and he wants him to lead the line next campaign.
And according to Spanish outlet OkDiario, Morata is desperate to resolve his future.
They reckon he wants to complete his United move this week to join the Red Devils' pre-season tour which starts on July 9.
OkDiario add that Morata doesn't want to link up with Real again when they return to training next Monday.
Real are said to be willing to sell the Spain international but they are demanding a £66m (€75m) fee.
The striker struggled to get game time under Zinedine Zidane last season but still managed to net 20 goals in all competitions.
Morata would become Mourinho's second summer signing.
The United boss has already landed Benfica defender Victor Lindelof in a £30m deal.
Mourinho is desperate to make signings with Champions League football returning to Old Trafford next season.
