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.