AS says United are willing to launch a transfer bid for Torres.
But they face competition from Real Madrid for the defender's signature.
And according to AS, the Red Devils may make an official bid in the coming weeks.
Torres, 24, enjoyed a fine season with boyhood club Villarreal and capped it off by lifting the Europa League, beating United in a marathon penalty shootout.
He has been with the club since 2002, aged just five, and has racked up 88 first-team appearances, earning himself a starting spot for Spain at Euro 2020.