The Spain international has spent his entire senior career with the La Liga giants after joining them from Gimnastic as a kid.
And he wrote his name into club folklore last season when he scored the decisive goal as Barcelona overcame a four-goal deficit to Paris Saint-Germain in the Champions League.
Roberto is under contract at the Nou Camp until 2019 but Barcelona are keen to tie him down for the long-term and increase his buyout clause.
The latest report from Spain suggests a stalemate in talks over a new deal may have opened the door for Jose Mourinho to make his move for the 25-year-old.
According to Diario Gol, the United gaffer 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.
Roberto’s agent has apparently presented a counter offer to Barcelona and their response will determine whether Mourinho is contacted.