Metro reports that United have been told the Spain Under-21 player is available for a bargain £6million.
United boss David Moyes is desperate to bring in an attacking midfielder in January after having failed to land Cesc Fabregas and Ander Herrera in the summer.
Roberto has just 18 months left on his current contract with Barcelona and his agent has offered him around.
The highly-rated midfielder reportedly interested in a January move to Old Trafford.
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.