Toffees boss Roberto Martinez is said to be targeting the out-of-favour Spaniard in a bid to bolster his midfield.
Roberto, 23, has made 77 total appearances for Barca since earning his professional debut in November 2010, while also adding seven goals and two assists.
The former Spain Under-21 international featured 27 times for the club last season under the since-departed Gerardo Martino, but has seen his first-team opportunities limited this term with the arrival of Luis Enrique.
Having made just 12 appearances in all competitions, he is now believed to have been told he can leave the Nou Camp at the end of the campaign, with Everton said to be the leading the pack to snap him up come the summer transfer window.
Toffees manager Roberto Martinez of course had another Barca product on loan at Goodison Park last season, in Gerard Deulofeu, and the Spaniard’s Catalan connections could help him broker another deal with the La Liga giants.
However, Stoke also came close to sealing Roberto’s signature in the winter market, per the Mirror, with former Barca striker Mark Hughes using his contacts at the club to sign the like of Marc Muniesa and Bojan Krkic in recent seasons.
The midfielder was even said to been keen on reuniting with his fellow La Masia graduates, although the move is believed to have broken down due to the Potters being unable to meet his wage demands.
Once hailed as Xavi’s heir, Roberto no doubt has the talent to succeed in the Premier League, despite falling behind Ivan Rakitic and Sergi Samper in the pecking order at Barca, and Everton could well be where he seeks to get his still-promising career back on track.