The Spanish club have offered the Dutch international a three-year contract, and all parties are optimistic about striking an agreement soon.
Depay will be a free agent after his contract expires with Lyon later this month, and he could prove to be a quality addition to the Barcelona attack.
The 27-year-old can operate as a wide forward as well as a centre forward, and his versatility will be an asset for Ronald Koeman.
The Barcelona manager has worked with Depay during their time together with the Netherlands national team, and he knows the strengths and weaknesses of the former Manchester United winger.
It is no secret that Barcelona will have to improve their attacking options, and Depay will be a massive upgrade on the likes of Braithwaite.
The Dutch international is at the peak of his career right now, and he could prove to be a major bargain on a free transfer.
The 27-year-old scored 22 goals and picked up 12 assists in the French league this past season, and he could form a little partnership with Antoine Griezmann and Lionel Messi in attack next season.
His arrival will also allow youngsters like Ansu Fati to develop at their own pace. The youngster was a first-team regular for Barcelona this past season before his injury blow, and the youngster will need to be eased back into the side next year.