Diario Gol says United is a long-term admirer of Roberto and wanted him over the summer.
And he could take advantage of his relatively modest £36m (€40m) buyout clause to get him on-board.
Barcelona are fighting hard to keep hold of Roberto and are offering a pay rise.
However, their current offer does not correspond with the £355m (€400m) buyout clause they want to insert into his new deal.
And United's willingness to double Roberto's current pay packet might tempt him into snubbing Barcelona and heading to Old Trafford.