El Mundo Deportivo reports that the Premier League rivals are preparing bids of around £17million for the 21-year-old midfielder.
Roberto remains out of favour with Barcelona boss Gerardo Martino and could be set to leave the club, who he has made just six appearances in La Liga for.
The youngster has an €20million release clause in his contract with Barcelona.
AC Milan are also reportedly keeping an eye on Roberto’s situation at Barcelona.
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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.