Spanish news outlet Don Balon say the Portuguese is keen to sign the versatile midfielder.
It’s suggested Mourinho is willing to give Roberto a hefty pay rise in a bid to lure him away from the Nou Camp.
The 25-year-old also has a tantalising £37.5m release clause which has fuelled speculation that he could be on the move.
Speaking in the summer Roberto said he was happy at Barca - provided he played in midfield throughout the campaign.
“In pre-season I wasn't starting,” he explained.
“But now in the official matches I am playing more.
“I want to continue here and continue like this."
Roberto can be deployed in midfield, at full-back or as a winger.
He played primarily at right-back last term and acquitted himself well.
However, the Spain international prefers to play in a more central attacking role.
Since making his debut in 2010, he’s struggled to establish himself as a regular starter.
Roberto has made 96 appearances for the club, scoring one goal.
Don Balon say Mourinho thinks Roberto is undervalued at Barca and would be a bargain for the Premier League heavyweights.
