The 21-year-old midfielder was a target for Tottenham earlier this year, but the Catalan giants rejected a loan bid for the talented Spain under-21 international from Spurs.
Manchester United tried and failed to sign Roberto's Barca teammate Cesc Fabregas in the summer window, while Bayern Munich - who beat United to Thiago Alcantara - are reportedly also monitoring Roberto.
The La Masia academy graduate has made just three substitute appearances in La Liga this season, and Barca boss Tata Martino has asked Roberto to bide his time at the Nou Camp and wait for a first-team opportunity.
But United manager David Moyes is keen to strengthen his midfield at the earliest opportunity in the January window, and Roberto is reportedly one of his top targets.
United snapped up Marouane Fellaini on the final day of the summer window, but the £27.5m signing suffered a wrist injury late last month and faces several weeks on the sidelines.
That injury has exposed United's frailty in midfield, with Moyes only able to call on Michael Carrick, Tom Cleverley and Anderson at present.
Roberto has made six league appearances for the Barca first-team since making his debut in 2010.