Maureen likes to have 3 or 4 quick, skillful and mobile runners available to play in behind a powerful central striker. He's had Willian, Hazard and Oscar fill the role for 2 seasons, and bought both Salah and Cuadrado (neither of whom has measured up, and both of whom are goners - in fact I think Salah has already, hasn't he?) to supplement them. There's also talk that Oscar is out of favour now as well and interesting Juventus, so whilst the Express might be just whistling in the dark about Sterling, I don't think you're right in your assertion that Chelsea wouldn't be interested. Plus he (Mourinho) would be sticking it to his closest rival, ie City, if he did move for the player.
Absurd price though it is, I want to get this signing wrapped up quick and then follow up with De Bruyne, as I don't think either Pogba or Wilshere will come.