According to MailOnline's Matt Barlow, Barca attempted to re-sign the winger for £10.5 million after triggering his buyback clause.
However, while the Spaniard is set to leave Everton this summer as he does not feature in manager Ronald Koeman's plans, he wants to join a club where he will play regular first-team football next season.
Deulofeu has been playing with Spain's youth side at the Under-21 European Championship this summer, though Yahoo Sports' Andrew Gaffney wasn't overly impressed with his performance against Italy in the semi-final:
BeIN Sports' David Cartlidge believes Barca would have been wise to keep Jordi Mboula—who has joined Monaco—rather than target Deulofeu:
The 23-year-old has had a mixed time since leaving the Camp Nou for Everton permanently in the summer of 2015.
He bagged 13 assists and four goals in all competitions in his first season, but last year he struggled under Koeman and was loaned out to Milan in January.
However, he gained a new lease of life with the Rossoneri, per GianlucaDiMarzio.com's David Amoyal:
Indeed, per WhoScored.com, despite only spending half a campaign in Italy, he showed off his impressive ability with the ball at his feet:
It's understandable that Milan want to bring him back to the club given his performances, and they'd arguably be a better option for him than Juve if regular minutes are his main priority.
Silverware beckons in Turin, but while he'd likely enjoy more game time than he would if returning to Barcelona, he's unlikely to play a key role.
Deulofeu still needs to work out some issues relating to his consistency, but when on form, he can be a very good player and would make a strong acquisition for Milan.